A comparison of structure-preserving integrators for discrete thermoelastic systems

Abstract

This paper contains a comparison of three recently proposed structure-preserving time-stepping schemes for nonlinear thermomechanical systems. These schemes can be considered as extension to coupled thermoelastic problems of well-established energy–momentum schemes for nonlinear elastodynamics. The present comparison is performed in the context of a finite-dimensional model problem for coupled thermomechanical systems: the thermoelastic double pendulum. It is shown that, similar to their purely mechanical ancestors, structure-preserving integrators for coupled thermoelasticity in general exhibit superior numerical stability and robustness properties.