Performance Assessment of Variational Integrators for Thermomechanical Problems

TL;DR

This paper evaluates variational integrators for thermo-viscoelastic systems with heat transfer, comparing their performance to Energy-Entropy-Momentum methods to assess robustness and stability in coupled dissipative problems.

Contribution

It extends Hamilton's principle to derive variational integrators for thermo-viscoelastic systems including heat transfer and viscosity, and compares their effectiveness with existing methods.

Findings

Variational integrators demonstrate robustness in coupled thermomechanical problems.

Comparison shows strengths and weaknesses relative to Energy-Entropy-Momentum methods.

Results highlight the potential of variational integrators for long-term stable simulations.

Abstract

Structure-preserving integrators are in the focus of ongoing research because of their distinguished features of robustness and long time stability. In particular, their formulation for coupled problems that include dissipative mechanisms is still an active topic. Conservative formulations, such as the thermo-elastic case without heat conduction, fit well into a variational framework and have been solved with variational integrators, whereas the inclusions of viscosity and heat transfer are still under investigation. To encompass viscous forces and heat transfer, an extension of Hamilton's principle is required. In this contribution we derive variational integrators for thermo-viscoelastic systems with classical heat transfer. Their results are compared for two discrete model problems vs. Energy-Entropy-Momentum methods. Such comparisons allow to draw conclusions about their relative performance, weaknesses and strengths.