Nonlinear electro-elastic finite element analysis with neural network constitutive models

Abstract: In the present work, the applicability of physics-augmented neural network (PANN) constitutive models for complex electro-elastic finite element analysis is demonstrated. For the investigations, PANN models for electro-elastic material behavior at finite deformations are calibrated to different synthetically generated datasets, including an analytical isotropic potential, a homogenised rank-one laminate, and a homogenised metamaterial with a spherical inclusion. Subsequently, boundary value problems inspired by engineering applications of composite electro-elastic materials are considered. Scenarios with large electrically induced deformations and instabilities are particularly challenging and thus necessitate extensive investigations of the PANN constitutive models in the context of finite element analyses. First of all, an excellent prediction quality of the model is required for very general load cases occurring in the simulation. Furthermore, simulation of large deformations and instabilities poses challenges on the stability of the numerical solver, which is closely related to the constitutive model. In all cases studied, the PANN models yield excellent prediction qualities and a stable numerical behavior even in highly nonlinear scenarios. This can be traced back to the PANN models excellent performance in learning both the first and second derivatives of the ground truth electro-elastic potentials, even though it is only calibrated on the first derivatives. Overall, this work demonstrates the applicability of PANN constitutive models for the efficient and robust simulation of engineering applications of composite electro-elastic materials.