2000 character limit reached
Hybrid data-driven and physics-informed regularized learning of cyclic plasticity with Neural Networks (2403.01776v1)
Published 4 Mar 2024 in cond-mat.mtrl-sci, cs.LG, nlin.AO, and physics.comp-ph
Abstract: An extendable, efficient and explainable Machine Learning approach is proposed to represent cyclic plasticity and replace conventional material models based on the Radial Return Mapping algorithm. High accuracy and stability by means of a limited amount of training data is achieved by implementing physics-informed regularizations and the back stress information. The off-loading of the Neural Network is applied to the maximal extent. The proposed model architecture is simpler and more efficient compared to existing solutions from the literature, while representing a complete three-dimensional material model. The validation of the approach is carried out by means of surrogate data obtained with the Armstrong-Frederick kinematic hardening model. The Mean Squared Error is assumed as the loss function which stipulates several restrictions: deviatoric character of internal variables, compliance with the flow rule, the differentiation of elastic and plastic steps and the associativity of the flow rule. The latter, however, has a minor impact on the accuracy, which implies the generalizability of the model for a broad spectrum of evolution laws for internal variables. Numerical tests simulating several load cases are shown in detail and validated for accuracy and stability.
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[2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. 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[2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bock, F.E., Aydin, R.C., Cyron, C.J., Huber, N., Kalidindi, S.R., Klusemann, B.: A review of the application of machine learning and data mining approaches in continuum materials mechanics. Frontiers in Materials 6 (2019) https://doi.org/10.3389/fmats.2019.00110 Lei et al. [2024] Lei, M., Sun, G., Yang, G., Wen, B.: A computational mechanical constitutive modeling method based on thermally-activated microstructural evolution and strengthening mechanisms. International Journal of Plasticity 173, 103881 (2024) https://doi.org/10.1016/j.ijplas.2024.103881 Miehe et al. [2010] Miehe, C., Hofacker, M., Welschinger, F.: A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering 199(45), 2765–2778 (2010) https://doi.org/10.1016/j.cma.2010.04.011 Aydiner et al. [2024] Aydiner, I.U., Tatli, B., Yalçinkaya, T.: Investigation of failure mechanisms in dual-phase steels through cohesive zone modeling and crystal plasticity frameworks. International Journal of Plasticity 174, 103898 (2024) https://doi.org/10.1016/j.ijplas.2024.103898 Bartošák and Horváth [2024] Bartošák, M., Horváth, J.: A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading. International Journal of Plasticity 173, 103868 (2024) https://doi.org/10.1016/j.ijplas.2023.103868 Hornik et al. [1989] Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lei, M., Sun, G., Yang, G., Wen, B.: A computational mechanical constitutive modeling method based on thermally-activated microstructural evolution and strengthening mechanisms. International Journal of Plasticity 173, 103881 (2024) https://doi.org/10.1016/j.ijplas.2024.103881 Miehe et al. [2010] Miehe, C., Hofacker, M., Welschinger, F.: A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering 199(45), 2765–2778 (2010) https://doi.org/10.1016/j.cma.2010.04.011 Aydiner et al. [2024] Aydiner, I.U., Tatli, B., Yalçinkaya, T.: Investigation of failure mechanisms in dual-phase steels through cohesive zone modeling and crystal plasticity frameworks. International Journal of Plasticity 174, 103898 (2024) https://doi.org/10.1016/j.ijplas.2024.103898 Bartošák and Horváth [2024] Bartošák, M., Horváth, J.: A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading. International Journal of Plasticity 173, 103868 (2024) https://doi.org/10.1016/j.ijplas.2023.103868 Hornik et al. [1989] Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Miehe, C., Hofacker, M., Welschinger, F.: A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering 199(45), 2765–2778 (2010) https://doi.org/10.1016/j.cma.2010.04.011 Aydiner et al. [2024] Aydiner, I.U., Tatli, B., Yalçinkaya, T.: Investigation of failure mechanisms in dual-phase steels through cohesive zone modeling and crystal plasticity frameworks. International Journal of Plasticity 174, 103898 (2024) https://doi.org/10.1016/j.ijplas.2024.103898 Bartošák and Horváth [2024] Bartošák, M., Horváth, J.: A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading. International Journal of Plasticity 173, 103868 (2024) https://doi.org/10.1016/j.ijplas.2023.103868 Hornik et al. [1989] Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aydiner, I.U., Tatli, B., Yalçinkaya, T.: Investigation of failure mechanisms in dual-phase steels through cohesive zone modeling and crystal plasticity frameworks. International Journal of Plasticity 174, 103898 (2024) https://doi.org/10.1016/j.ijplas.2024.103898 Bartošák and Horváth [2024] Bartošák, M., Horváth, J.: A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading. International Journal of Plasticity 173, 103868 (2024) https://doi.org/10.1016/j.ijplas.2023.103868 Hornik et al. [1989] Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bartošák, M., Horváth, J.: A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading. International Journal of Plasticity 173, 103868 (2024) https://doi.org/10.1016/j.ijplas.2023.103868 Hornik et al. [1989] Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. 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Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. 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Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. 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Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. 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Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. 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International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. 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Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Miehe, C., Hofacker, M., Welschinger, F.: A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering 199(45), 2765–2778 (2010) https://doi.org/10.1016/j.cma.2010.04.011 Aydiner et al. [2024] Aydiner, I.U., Tatli, B., Yalçinkaya, T.: Investigation of failure mechanisms in dual-phase steels through cohesive zone modeling and crystal plasticity frameworks. International Journal of Plasticity 174, 103898 (2024) https://doi.org/10.1016/j.ijplas.2024.103898 Bartošák and Horváth [2024] Bartošák, M., Horváth, J.: A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading. International Journal of Plasticity 173, 103868 (2024) https://doi.org/10.1016/j.ijplas.2023.103868 Hornik et al. [1989] Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aydiner, I.U., Tatli, B., Yalçinkaya, T.: Investigation of failure mechanisms in dual-phase steels through cohesive zone modeling and crystal plasticity frameworks. International Journal of Plasticity 174, 103898 (2024) https://doi.org/10.1016/j.ijplas.2024.103898 Bartošák and Horváth [2024] Bartošák, M., Horváth, J.: A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading. International Journal of Plasticity 173, 103868 (2024) https://doi.org/10.1016/j.ijplas.2023.103868 Hornik et al. [1989] Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bartošák, M., Horváth, J.: A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading. International Journal of Plasticity 173, 103868 (2024) https://doi.org/10.1016/j.ijplas.2023.103868 Hornik et al. [1989] Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. 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Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839
- Lei, M., Sun, G., Yang, G., Wen, B.: A computational mechanical constitutive modeling method based on thermally-activated microstructural evolution and strengthening mechanisms. International Journal of Plasticity 173, 103881 (2024) https://doi.org/10.1016/j.ijplas.2024.103881 Miehe et al. [2010] Miehe, C., Hofacker, M., Welschinger, F.: A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering 199(45), 2765–2778 (2010) https://doi.org/10.1016/j.cma.2010.04.011 Aydiner et al. [2024] Aydiner, I.U., Tatli, B., Yalçinkaya, T.: Investigation of failure mechanisms in dual-phase steels through cohesive zone modeling and crystal plasticity frameworks. 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International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Miehe, C., Hofacker, M., Welschinger, F.: A phase field model for rate-independent crack propagation: Robust algorithmic implementation based on operator splits. Computer Methods in Applied Mechanics and Engineering 199(45), 2765–2778 (2010) https://doi.org/10.1016/j.cma.2010.04.011 Aydiner et al. [2024] Aydiner, I.U., Tatli, B., Yalçinkaya, T.: Investigation of failure mechanisms in dual-phase steels through cohesive zone modeling and crystal plasticity frameworks. International Journal of Plasticity 174, 103898 (2024) https://doi.org/10.1016/j.ijplas.2024.103898 Bartošák and Horváth [2024] Bartošák, M., Horváth, J.: A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading. International Journal of Plasticity 173, 103868 (2024) https://doi.org/10.1016/j.ijplas.2023.103868 Hornik et al. [1989] Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aydiner, I.U., Tatli, B., Yalçinkaya, T.: Investigation of failure mechanisms in dual-phase steels through cohesive zone modeling and crystal plasticity frameworks. International Journal of Plasticity 174, 103898 (2024) https://doi.org/10.1016/j.ijplas.2024.103898 Bartošák and Horváth [2024] Bartošák, M., Horváth, J.: A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading. International Journal of Plasticity 173, 103868 (2024) https://doi.org/10.1016/j.ijplas.2023.103868 Hornik et al. [1989] Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bartošák, M., Horváth, J.: A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading. International Journal of Plasticity 173, 103868 (2024) https://doi.org/10.1016/j.ijplas.2023.103868 Hornik et al. [1989] Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. 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[2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. 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Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. 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International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. 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[1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. 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Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bartošák, M., Horváth, J.: A continuum damage coupled unified viscoplastic model for simulating the mechanical behaviour of a ductile cast iron under isothermal low-cycle fatigue, fatigue-creep and creep loading. International Journal of Plasticity 173, 103868 (2024) https://doi.org/10.1016/j.ijplas.2023.103868 Hornik et al. [1989] Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. 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[2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. 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International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. 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Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. 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Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hornik, K., Stinchcombe, M., White, H.: Multilayer feedforward networks are universal approximators. Neural Networks 2(5), 359–366 (1989) https://doi.org/10.1016/0893-6080(89)90020-8 Raissi et al. [2019] Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Raissi, M., Perdikaris, P., Karniadakis, G.E.: Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics 378, 686–707 (2019) https://doi.org/10.1016/j.jcp.2018.10.045 Kollmannsberger [2021] Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. 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Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. 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Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. 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Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. 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Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. 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[2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. 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Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. 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Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. 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[2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. 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Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. 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International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. 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[1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. 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International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Kollmannsberger, S.: Deep Learning in Computational Mechanics: an Introductory Course. Studies in computational intelligence. Springer, Cham (2021). https://link.springer.com/10.1007/978-3-030-76587-3 Hildebrand and Klinge [2023] Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. 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Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. 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[1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. 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Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. 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Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. 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International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Hildebrand, S., Klinge, S.: Comparison of Neural FEM and Neural Operator Methods for applications in Solid Mechanics (2023) Bock et al. [2021] Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. 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Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839
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[2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bock, F.E., Keller, S., Huber, N., Klusemann, B.: Hybrid modelling by machine learning corrections of analytical model predictions towards high-fidelity simulation solutions. Materials 14(8) (2021) https://doi.org/10.3390/ma14081883 Simo and Hughes [1998] Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. 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Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. 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Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. 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Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Simo, J.C., Hughes, T.J.R.: Computational Inelasticity. Interdisciplinary Applied Mathematics, vol. 7. Springer, New York, Berlin, Heidelberg (1998) Khan and Huang [1995] Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Khan, A.S., Huang, S.: Continuum Theory of Plasticity. John Wiley and Sons, Inc., New York, Chichester, Brisbane, Toronto, Singapore (1995) Bland [1957] Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. 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Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. 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[1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bland, D.R.: The associated flow rule of plasticity. Journal of the Mechanics and Physics of Solids 6(1), 71–78 (1957) https://doi.org/10.1016/0022-5096(57)90049-2 Suchocki [2022] Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. 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International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. 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[1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. 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Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Suchocki, C.: On finite element implementation of cyclic elastoplasticity: theory, coding, and exemplary problems. Acta Mechanica 233, 83–120 (2022) https://doi.org/10.1007/s00707-021-03069-3 Frederick and Armstrong [2007] Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. 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Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. 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International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. 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[1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. 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Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839
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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Frederick, C.O., Armstrong, P.J.: A mathematical representation of the multiaxial bauschinger effect. Materials at High Temperatures 24, 1–26 (2007) Aygün et al. [2021] Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. 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Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Aygün, S., Wiegold, T., Klinge, S.: Coupling of the phase field approach to the armstrong-frederick model for the simulation of ductile damage under cyclic load. International Journal of Plasticity 143, 103021 (2021) https://doi.org/10.1016/j.ijplas.2021.103021 Furukawa and Hoffman [2004] Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. 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Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. 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Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Furukawa, T., Hoffman, M.: Accurate cyclic plastic analysis using a neural network material model. Engineering Analysis with Boundary Elements 28(3), 195–204 (2004) https://doi.org/10.1016/S0955-7997(03)00050-X Gorji et al. [2020] Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. 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International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. 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Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. 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Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. 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[2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839
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International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Gorji, M.B., Mozaffar, M., Heidenreich, J.N., Cao, J., Mohr, D.: On the potential of recurrent neural networks for modeling path dependent plasticity. Journal of the Mechanics and Physics of Solids 143, 103972 (2020) https://doi.org/10.1016/j.jmps.2020.103972 Jang et al. [2021] Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Jang, D.P., Fazily, P., Yoon, J.W.: Machine learning-based constitutive model for j2- plasticity. International Journal of Plasticity 138, 102919 (2021) https://doi.org/10.1016/j.ijplas.2020.102919 Huang et al. [2020] Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. 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Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. 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Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. 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International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. 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[1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Huang, D., Fuhg, J.N., Weißenfels, C., Wriggers, P.: A machine learning based plasticity model using proper orthogonal decomposition. Computer Methods in Applied Mechanics and Engineering 365, 113008 (2020) https://doi.org/10.1016/j.cma.2020.113008 Logarzo et al. [2021] Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. 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Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Logarzo, H.J., Capuano, G., Rimoli, J.J.: Smart constitutive laws: Inelastic homogenization through machine learning. Computer Methods in Applied Mechanics and Engineering 373, 113482 (2021) https://doi.org/10.1016/j.cma.2020.113482 Cho et al. [2014] Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. 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Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. 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[2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839
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Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Cho, K., Merrienboer, B., Bahdanau, D., Bengio, Y.: On the properties of neural machine translation: Encoder-decoder approaches. CoRR abs/1409.1259 (2014) 1409.1259 Bonatti and Mohr [2021] Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Bonatti, C., Mohr, D.: One for all: Universal material model based on minimal state-space neural networks. Science Advances 7(26), 3658 (2021) https://doi.org/10.1126/sciadv.abf3658 https://www.science.org/doi/pdf/10.1126/sciadv.abf3658 Joudivand Sarand and Misirlioglu [2024] Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Joudivand Sarand, M.H., Misirlioglu, I.B.: A physics-based plasticity study of the mechanism of inhomogeneous strain evolution in dual phase 600 steel. International Journal of Plasticity 174, 103918 (2024) https://doi.org/10.1016/j.ijplas.2024.103918 Linka et al. [2021] Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. 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[2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. 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Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. 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Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. 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[1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. 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International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. 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In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. 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[1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. Computational Mechanics (2024) Lubliner et al. [1989] Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. [2021b] Wang, S., Wang, H., Perdikaris, P.: Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets. arXiv (2021). https://doi.org/10.48550/ARXIV.2103.10974 . https://arxiv.org/abs/2103.10974 Fuhg and Bouklas [2022] Fuhg, J.N., Bouklas, N.: The mixed deep energy method for resolving concentration features in finite strain hyperelasticity. Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Lubliner, J., Oliver, J., Oller, S., Oñate, E.: A plastic-damage model for concrete. International Journal of Solids and Structures 25(3), 299–326 (1989) https://doi.org/10.1016/0020-7683(89)90050-4 Vacev et al. [2023] Vacev, T., Zorić, A., Grdić, D., Ristić, N., Grdić, Z., Milić, M.: Experimental and numerical analysis of impact strength of concrete slabs. Periodica Polytechnica Civil Engineering 67(1), 325–335 (2023) https://doi.org/10.3311/PPci.21084 Oliveira and Penna [2004] Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. In: Autodiff Workshop NIPS 2017 (2017). https://api.semanticscholar.org/CorpusID:40027675 Nguyen-Thanh et al. [2020] Nguyen-Thanh, V.M., Zhuang, X., Rabczuk, T.: A deep energy method for finite deformation hyperelasticity. European Journal of Mechanics - A/Solids 80, 103874 (2020) https://doi.org/10.1016/j.euromechsol.2019.103874 [40] Krishnapriyan, A., Gholami, A., Zhe, S., Kirby, R., Mahoney, M.W.: Characterizing possible failure modes in physics-informed neural networks. In: Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P.S., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems, vol. 34, pp. 26548–26560. Curran Associates, Inc. https://proceedings.neurips.cc/paper/2021/file/df438e5206f31600e6ae4af72f2725f1-Paper.pdf Wang et al. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Hillgärtner, M., Abdolazizi, K.P., Aydin, R.C., Itskov, M., Cyron, C.J.: Constitutive artificial neural networks: A fast and general approach to predictive data-driven constitutive modeling by deep learning. Journal of Computational Physics 429, 110010 (2021) https://doi.org/10.1016/j.jcp.2020.110010 As’ad et al. [2022] As’ad, F., Avery, P., Farhat, C.: A mechanics-informed artificial neural network approach in data-driven constitutive modeling. International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. 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International Journal for Numerical Methods in Engineering 123(12), 2738–2759 (2022) https://doi.org/10.1002/nme.6957 https://onlinelibrary.wiley.com/doi/pdf/10.1002/nme.6957 Linka and Kuhl [2023] Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Linka, K., Kuhl, E.: A new family of constitutive artificial neural networks towards automated model discovery. Computer Methods in Applied Mechanics and Engineering 403, 115731 (2023) https://doi.org/10.1016/j.cma.2022.115731 Zhang and Mohr [2020] Zhang, A., Mohr, D.: Using neural networks to represent von mises plasticity with isotropic hardening. International Journal of Plasticity 132, 102732 (2020) https://doi.org/10.1016/j.ijplas.2020.102732 Shoghi and Hartmaier [2022] Shoghi, R., Hartmaier, A.: Optimal data-generation strategy for machine learning yield functions in anisotropic plasticity. Frontiers in Materials 9 (2022) https://doi.org/10.3389/fmats.2022.868248 Shoghi et al. [2024] Shoghi, R., Morand, L., Helm, D., Hartmaier, A.: Optimizing machine learning yield functions using query-by-committee for support vector classification with a dynamic stopping criterion. 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Journal of Computational Physics 451, 110839 (2022) https://doi.org/10.1016/j.jcp.2021.110839 Oliveira, D.B., Penna, S.S.: A general framework for finite strain elastoplastic models: a theoretical approach. Journal of the Brazilian Society of Mechanical Sciences and Engineering 44, 87–116 (2004) https://doi.org/10.1007/s40430-022-03647-z Dettmer and Reese [2004] Dettmer, W., Reese, S.: On the theoretical and numerical modelling of armstrong–frederick kinematic hardening in the finite strain regime. Computer Methods in Applied Mechanics and Engineering 193(1), 87–116 (2004) https://doi.org/10.1016/j.cma.2003.09.005 Kingma and Ba [2014] Kingma, D.P., Ba, J.: Adam: A Method for Stochastic Optimization. arXiv (2014). https://doi.org/10.48550/ARXIV.1412.6980 . https://arxiv.org/abs/1412.6980 Paszke et al. [2017] Paszke, A., Gross, S., Chintala, S., Chanan, G., Yang, E., DeVito, Z., Lin, Z., Desmaison, A., Antiga, L., Lerer, A.: Automatic differentiation in pytorch. 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