Development of consistent simulation methods for electrothermomechanically coupled systems

本建议的重点是发展一致和有效的电-热-机械耦合系统的模拟方法。假定有限变形和非线性本构律。在资助阶段，将研究电-热-粘-弹-动力耦合系统，并开发有效的数值方法。应用的例子是电活性聚合物和介电弹性体。采用特殊有限元方法的类湖-水-祖混合公式和随后的静态凝结，以及保持结构的积分器，可以获得先进的、一致的、高效的模拟方法，这些方法在时间离散设置下也与力学平衡方程和热力学定律保持一致。使用泛型形式和多凸启发的张量叉积公式等方法极大地简化了方程的结构，并便于结构保持积分器的设计。此外，从多凸启发框架获得的离散梯度具有特别简单的形状，这与经典的基于投影的离散梯度形成鲜明对比。

This proposal focuses on the development of consistent and efficient simulation methods for electrothermomechanically coupled systems. Finite deformations and nonlinear constitutive laws are assumed. In the funding phase, electrothermoviscoelastodynamically coupled systems will be investigated and efficient numerical methods will be developed. Examples of applications are electroactive polymers and dielectric elastomers in particular. Advanced consistent and efficient simulation methods can be obtained on the one hand by mixed Hu-Washizu-like formulations with special FE approaches and subsequent static condensation and on the other hand by structure-preserving integrators, which are also consistent in the time discrete setting with respect to the mechanical balance equations as well as the laws of thermodynamics. Methods such as GENERIC formalism and polyconvex-inspired formulations using the tensor cross product significantly simplify the structure of the equations and facilitate the design of structure-preserving integrators. In addition, discrete gradients obtained from polyconvexity-inspired frameworks are characterized by a particularly simple shape which is in stark contrast to classic projection-based discrete gradients.