Development of consistent simulation methods for electrothermomechanically coupled systems

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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.