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 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.

中文翻译：

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基于神经网络本构模型的非线性电弹性有限元分析

在目前的工作中，证明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。为了进行研究，有限变形下电弹性材料行为的 PANN 模型被校准为描述介电弹性体本构响应的不同综合生成的数据集。其中包括分析各向同性势、均质一级层压板和具有球形夹杂物的均质超材料。随后，考虑了复合电弹性材料工程应用启发的边值问题。具有较大电致变形和不稳定性的场景尤其具有挑战性，因此需要在有限元分析的背景下对 PANN 本构模型进行广泛研究。首先，对于模拟中发生的非常一般的负载情况，需要模型具有出色的预测质量。此外，大变形和不稳定性的模拟对与本构模型密切相关的数值求解器的稳定性提出了挑战。在所有研究的案例中，即使在高度非线性的情况下，PANN 模型也能产生出色的预测质量和稳定的数值行为。这可以追溯到 PANN 模型在学习地面真实电弹性势的一阶和二阶导数方面的出色性能，尽管它仅在一阶导数上进行了校准。总的来说，这项工作证明了 PANN 本构模型对于复合电弹性材料工程应用的高效和鲁棒模拟的适用性。