Structure-Preserving Discretization of a Polyconvexity-Inspired Formulation for Coupled Nonlinear Electro-Thermo-Elastodynamics

A consistent, structure-preserving space-time discretization for coupled nonlinear electro-thermo-elastodynamical problems is presented. The underlying polyconvexity-inspired mixed framework is facilitated by the properties of the tensor cross product. The elastodynamic problem is then extended by the energy balance as well as Gauss’s and Faraday’s law to integrate the thermodynamic and electrostatic contribution, respectively. A suitable polyconvexity-inspired internal energy function is chosen to complete the nonlinear, fully coupled electro-thermo-elastodynamical formulation. Additionally, we present a structure-preserving, second-order accurate time integration scheme, utilizing discrete derivatives in the sense of Gonzalez (1996), ensuring a stable and robust simulation even for large time steps. Finally, we assess the numerical performance of our newly developed method through representative examples also showing the possibilities of the framework in the field of boundary control.