A Novel Energy and Momentum Consistent Mixed Formulation for Coupled Nonlinear Electro‐Thermo‐Elastodynamics

Abstract

AbstractIn the present contribution, a novel mixed formulation aimed at the energy‐momentum consistent simulation of coupled nonlinear electro‐thermo‐elastodynamic systems, in particular dielectric elastomer actuators, is proposed. It is essentially based on a mixed framework for elastodynamics in the case of polyconvex stored energy functions. In accordance with this framework, the properties of the rediscovered tensor cross product are exploited in a first step to derive a mixed formulation via a Hu‐Washizu type extension of the stored energy function. Afterwards, the corresponding strong form is derived and supplemented with the (initial) boundary value problems of thermodynamics and electrostatics. By additionally choosing an appropriate polyconvexity‐inspired energy density function, this procedure leads to a fully coupled electro‐thermo‐elastodynamic formulation that benefits from the properties of the underlying mixed framework.Furthermore, an energy‐momentum consistent time integration scheme is proposed for the novel framework, where discrete derivatives in the sense of Gonzalez are employed. The formulation is second‐order accurate and stable even for large time step sizes. Eventually, the performance of the novel formulation is illustrated in a numerical example.