Frame-indifferent discretization in nonlinear thermoviscoelasticity: Analysis and numerical simulations

TL;DR

This paper refines discretization schemes for nonlinear thermoviscoelasticity models to ensure frame indifference at a time-discrete level, with analytical and numerical validation.

Contribution

It introduces a discretization approach that enforces frame indifference during time discretization, improving upon previous methods.

Findings

Discretization scheme respects frame indifference analytically.

Numerical simulations confirm the scheme's effectiveness.

Enhanced stability and physical consistency in simulations.

Abstract

We consider a quasi-static nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations. We refine the discretization schemes in [Badal-Friedrich-Kru\v{z}\'ik '23, Mielke-Roub\'{\i}\v{c}ek '20] by imposing frame indifference already at a time-discrete level. This is justified both analytically and numerically.