GENERIC-based formulation and discretization of initial boundary value problems for finite strain thermoelasticity

Abstract

A new variational formulation for finite strain thermoelastodynamics is proposed. The variational formulation emanates from the GENERIC formalism and makes possible the free choice of the thermodynamic state variable. In particular, one may choose the absolute temperature, the internal energy density or the entropy density as state variable. To solve initial boundary value problems, the GENERIC formalism is extended to open systems. The discretization in time makes use of the standard mid-point rule. Depending on the choice of the thermodynamic state variable structure-preserving schemes are obtained. For example, choosing the internal energy as state variable yields a new energy–momentum consistent scheme. Thus the newly developed GENERIC-based weak form is particularly well suited for the design of structure-preserving methods. Numerical investigations are presented which confirm the theoretical findings and shed light on the numerical stability of the newly developed schemes.