A novel mixed and energy‐momentum consistent framework for coupled nonlinear thermo‐electro‐elastodynamics

Abstract

AbstractA novel mixed framework and energy‐momentum consistent integration scheme in the field of coupled nonlinear thermo‐electro‐elastodynamics is proposed. The mixed environment is primarily based on a framework for elastodynamics in the case of polyconvex strain energy functions. For this elastodynamic framework, the properties of the so‐called tensor cross product are exploited to derive a mixed formulation via a Hu‐Washizu type extension of the strain energy function. Afterwards, a general path to incorporate nonpotential problems for mixed formulations is demonstrated. To this end, the strong form of the mixed framework is derived and supplemented with the energy balance as well as Maxwell's equations neglecting magnetic and time dependent effects. By additionally choosing an appropriate energy function, this procedure leads to a fully coupled thermo‐electro‐elastodynamic formulation which benefits from the properties of the underlying mixed framework. In addition, the proposed mixed framework facilitates the design of a new energy‐momentum consistent time integration scheme by employing discrete derivatives in the sense of Gonzalez. A one‐step integration scheme of second‐order accuracy is obtained which is shown to be stable even for large time steps. Eventually, the performance of the novel formulation is demonstrated in several numerical examples.