Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
184 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A novel section-section potential for short-range interactions between plane beams (2404.04408v1)

Published 5 Apr 2024 in cs.CE

Abstract: We derive a novel formulation for the interaction potential between deformable fibers due to short-range fields arising from intermolecular forces. The formulation improves the existing section-section interaction potential law for in-plane beams by considering an offset between interacting cross sections. The new law is asymptotically consistent, which is particularly beneficial for computationally demanding scenarios involving short-range interactions like van der Waals and steric forces. The formulation is implemented within a framework of rotation-free Bernoulli-Euler beams utilizing the isogeometric paradigm. The improved accuracy of the novel law is confirmed through thorough numerical studies. We apply the developed formulation to investigate the complex behavior observed during peeling and pull-off of elastic fibers interacting via the Lennard-Jones potential.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (40)
  1. M. P. Murrell and M. L. Gardel, “F-actin buckling coordinates contractility and severing in a biomimetic actomyosin cortex,” Proceedings of the National Academy of Sciences, vol. 109, no. 51, pp. 20820–20825, 2012.
  2. V. M. Slepukhin, M. J. Grill, Q. Hu, E. Botvinick, W. Wall, and A. Levine, “Topological defects produce kinks in biopolymer filament bundles,” Proceedings of the National Academy of Sciences, vol. 118, no. 15, 2021.
  3. H. G. Franquelim, A. Khmelinskaia, J.-P. Sobczak, H. Dietz, and P. Schwille, “Membrane sculpting by curved DNA origami scaffolds,” Nature Communications, vol. 9, no. 1, p. 811, 2018.
  4. Y. Nishiyama, “Molecular interactions in nanocellulose assembly,” Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 376, no. 2112, p. 20170047, 2018.
  5. M. R. Islam, G. Tudryn, R. Bucinell, L. Schadler, and R. C. Picu, “Morphology and mechanics of fungal mycelium,” Scientific Reports, vol. 7, no. 1, p. 13070, 2017.
  6. A. Alavinasab, R. Jha, G. Ahmadi, C. Cetinkaya, and I. Sokolov, “Computational modeling of nano-structured glass fibers,” Computational Materials Science, vol. 44, no. 2, pp. 622–627, 2008.
  7. J.-K. Yoo, J. Kim, Y. Jung, and K. Kang, “Scalable fabrication of silicon nanotubes and their application to energy storage,” Advanced Materials, vol. 24, no. 40, pp. 5452–5456, 2012.
  8. M. Čanadija, “Deep learning framework for carbon nanotubes: mechanical properties and modeling strategies,” Carbon, 2021.
  9. P. Wriggers, Computational Contact Mechanics. Berlin Heidelberg: Springer-Verlag, 2006.
  10. J. N. Israelachvili, Intermolecular and surface forces - 3rd Edition. Academic Press, 2011.
  11. C. Argento, A. Jagota, and W. C. Carter, “Surface formulation for molecular interactions of macroscopic bodies,” Journal of the Mechanics and Physics of Solids, vol. 45, no. 7, pp. 1161–1183, 1997.
  12. R. A. Sauer and S. Li, “A contact mechanics model for quasi-continua,” International Journal for Numerical Methods in Engineering, vol. 71, no. 8, pp. 931–962, 2007.
  13. R. A. Sauer and S. Li, “An atomistically enriched continuum model for nanoscale contact mechanics and its application to contact scaling,” Journal of Nanoscience and Nanotechnology, vol. 8, no. 7, pp. 3757–3773, 2008.
  14. H. Fan and S. Li, “A three-dimensional surface stress tensor formulation for simulation of adhesive contact in finite deformation,” International Journal for Numerical Methods in Engineering, vol. 107, no. 3, pp. 252–270, 2016.
  15. R. A. Sauer and L. De Lorenzis, “A computational contact formulation based on surface potentials,” Computer Methods in Applied Mechanics and Engineering, vol. 253, pp. 369–395, 2013.
  16. T. X. Duong and R. A. Sauer, “A concise frictional contact formulation based on surface potentials and isogeometric discretization,” Computational Mechanics, vol. 64, no. 4, pp. 951–970, 2019.
  17. R. A. Sauer, “Multiscale modelling and simulation of the deformation and adhesion of a single gecko seta,” Computer Methods in Biomechanics and Biomedical Engineering, vol. 12, no. 6, pp. 627–640, 2009.
  18. R. A. Sauer, “A Computational Model for Nanoscale Adhesion between Deformable Solids and Its Application to Gecko Adhesion,” Journal of Adhesion Science and Technology, vol. 24, no. 11-12, pp. 1807–1818, 2010.
  19. R. A. Sauer and J. C. Mergel, “A geometrically exact finite beam element formulation for thin film adhesion and debonding,” Finite Elements in Analysis and Design, vol. 86, pp. 120–135, 2014.
  20. R. A. Sauer, “The Peeling Behavior of Thin Films with Finite Bending Stiffness and the Implications on Gecko Adhesion,” The Journal of Adhesion, vol. 87, no. 7-8, pp. 624–643, 2011.
  21. J. C. Mergel, R. A. Sauer, and A. Saxena, “Computational optimization of adhesive microstructures based on a nonlinear beam formulation,” Structural and Multidisciplinary Optimization, vol. 50, no. 6, pp. 1001–1017, 2014.
  22. J. C. Mergel and R. A. Sauer, “On the Optimum Shape of Thin Adhesive Strips for Various Peeling Directions,” The Journal of Adhesion, vol. 90, no. 5-6, pp. 526–544, 2014.
  23. C. Cyron and W. Wall, “Finite-element approach to Brownian dynamics of polymers,” Physical Review E, vol. 80, no. 6, p. 066704, 2009.
  24. C. J. Cyron, K. W. Müller, K. M. Schmoller, A. R. Bausch, W. A. Wall, and R. F. Bruinsma, “Equilibrium phase diagram of semi-flexible polymer networks with linkers,” EPL (Europhysics Letters), vol. 102, no. 3, p. 38003, 2013.
  25. C. Cyron, K. Müller, A. Bausch, and W. Wall, “Micromechanical simulations of biopolymer networks with finite elements,” Journal of Computational Physics, vol. 244, pp. 236–251, 2013.
  26. K. Müller, R. Bruinsma, O. Lieleg, A. Bausch, W. Wall, and A. Levine, “Rheology of semiflexible bundle networks with transient linkers,” Physical Review Letters, vol. 112, no. 23, p. 238102, 2014.
  27. M. J. Grill, W. A. Wall, and C. Meier, “A computational model for molecular interactions between curved slender fibers undergoing large 3D deformations with a focus on electrostatic, van der Waals, and repulsive steric forces,” International Journal for Numerical Methods in Engineering, vol. 121, no. 10, pp. 2285–2330, 2020.
  28. M. J. Grill, C. Meier, and W. A. Wall, “Investigation of the peeling and pull-off behavior of adhesive elastic fibers via a novel computational beam interaction model,” The Journal of Adhesion, vol. 97, no. 8, pp. 730–759, 2021.
  29. C. Meier, M. J. Grill, and W. A. Wall, “Generalized section-section interaction potentials in the geometrically exact beam theory: Modeling of intermolecular forces, asymptotic limit as strain-energy function, and formulation of rotational constraints,” International Journal of Solids and Structures, p. 112255, 2023.
  30. M. J. Grill, W. A. Wall, and C. Meier, “Analytical disk–cylinder interaction potential laws for the computational modeling of adhesive, deformable (nano)fibers,” International Journal of Solids and Structures, vol. 269, p. 112175, 2023.
  31. M. J. Grill, W. A. Wall, and C. Meier, “Asymptotically consistent and computationally efficient modeling of short-ranged molecular interactions between curved slender fibers undergoing large 3D deformations,” 2022.
  32. A. Borković, B. Marussig, and G. Radenković, “Geometrically exact static isogeometric analysis of arbitrarily curved plane Bernoulli–Euler beam,” Thin-Walled Structures, vol. 170, p. 108539, 2022.
  33. A. Borković, B. Marussig, and G. Radenković, “Geometrically exact static isogeometric analysis of an arbitrarily curved spatial Bernoulli–Euler beam,” Computer Methods in Applied Mechanics and Engineering, vol. 390, p. 114447, 2022.
  34. A. Borković, M. H. Gfrerer, and B. Marussig, “Geometrically exact isogeometric Bernoulli–Euler beam based on the Frenet–Serret frame,” Computer Methods in Applied Mechanics and Engineering, vol. 405, p. 115848, 2023.
  35. A. Borković, S. Kovačević, G. Radenković, S. Milovanović, and M. Guzijan-Dilber, “Rotation-free isogeometric analysis of an arbitrarily curved plane Bernoulli–Euler beam,” Computer Methods in Applied Mechanics and Engineering, vol. 334, pp. 238–267, 2018.
  36. D. Langbein, “Van der Waals attraction between cylinders, rods or fibers,” Physik der kondensierten Materie, vol. 15, no. 1, pp. 61–86, 1972.
  37. W. Research, “Mathematica.” Wolfram Research, Inc., 2024.
  38. D. Magisano, L. Leonetti, and G. Garcea, “How to improve efficiency and robustness of the Newton method in geometrically non-linear structural problem discretized via displacement-based finite elements,” Computer Methods in Applied Mechanics and Engineering, vol. 313, pp. 986–1005, 2017.
  39. R. A. Sauer, “Enriched contact finite elements for stable peeling computations,” International Journal for Numerical Methods in Engineering, vol. 87, no. 6, pp. 593–616, 2011.
  40. P. Gangl and M. H. Gfrerer, “A Unified Approach to Shape and Topological Sensitivity Analysis of Discretized Optimal Design Problems,” Applied Mathematics & Optimization, vol. 88, no. 2, p. 46, 2023.

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now