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

作者：Dominik K. Klein, Rogelio Ortigosa, Jesús Martínez‐Frutos, Oliver Weeger · 发表于：Computer Methods in Applied Mechanics and Engineering · 年份：2024 · DOI：10.1016/j.cma.2024.116910 · 被引用次数：18 · 研究领域：Dielectric materials and actuators、Vibration Control and Rheological Fluids、Ferroelectric and Piezoelectric Materials

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 describing the constitutive response of dielectric elastomers. These include 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 ...