Energy-momentum scheme for nonlinear thermo-electro-elastodynamics

The present contribution aims at the consistent discretisation of nonlinear, coupled thermoelectro-elastodynamics. In that regard, a new one-step implicit and thermodynamically consistent energymomentum integration scheme for the simulation of thermo-electro-elastic processes undergoing large deformations will be presented. The consideration is based upon polyconvexity inspired, constitutive models and a new tensor cross product algebra, which facilitate the design of the so-called discrete derivatives. The discrete derivatives are fundamental for the algorithmic evaluation of stresses and other derived variables like entropy density or the absolute temperature leading to a structure preserving integration scheme. In particular, recently published works of the authors concerning consistent time integration of large deformation thermo-elastodynamics and electro-elastodynamics are combined to a unified integration scheme. Numerical computations demonstrate the stability and conservation properties of the proposed energy-momentum scheme.