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.

翻译：本文展示了物理增强神经网络（PANN）本构模型在复杂电弹性有限元分析中的适用性。研究中，针对有限变形下电弹性材料行为的PANN模型被校准至多个合成生成的数据集，包括解析各向同性势、均质化秩一层压板以及含球形夹杂的均质化超材料。随后，研究了受复合电弹性材料工程应用启发的边值问题。大电致变形与失稳场景尤其具有挑战性，因此需要在有限元分析背景下对PANN本构模型进行深入探讨。首先，模型需对仿真中出现的极一般载荷情况具备优异的预测质量。此外，大变形与失稳的模拟对数值求解器的稳定性提出了挑战，而这与本构模型密切相关。在所研究的所有案例中，PANN模型均展现出优异的预测质量，即使在高度非线性场景下也能保持稳定的数值行为。这归因于PANN模型在学习真实电弹性势的一阶和二阶导数方面的卓越性能，尽管其仅基于一阶导数进行校准。总体而言，本工作证明了PANN本构模型在高效鲁棒仿真复合电弹性材料工程应用中的可行性。