A discrete variational scheme for isentropic processes in polyconvex thermoelasticity

TL;DR

This paper introduces a variational scheme for modeling isentropic processes in polyconvex thermoelasticity, ensuring energy dissipation and convergence under smooth conditions, advancing numerical methods in thermoelasticity.

Contribution

It develops a novel variational scheme embedding thermoelastic equations into a hyperbolic system, with proven existence of minimizers and convergence results.

Findings

Existence of minimizers for the variational scheme

Construction of measure-valued solutions dissipating energy

Convergence of the scheme for smooth solutions

Abstract

We propose a variational scheme for the construction of isentropic processes of the equations of adiabatic thermoelasticity with polyconvex internal energy. The scheme hinges on the embedding of the equations of adiabatic polyconvex thermoelasticity into a symmetrizable hyperbolic system. We establish existence of minimizers for an associated minimization theorem and construct measure-valued solutions that dissipate the total energy. We prove that the scheme converges when the limiting solution is smooth.