# Thermoviscoelasticity in Kelvin-Voigt rheology at large strains

## TL;DR

This paper develops a thermodynamically consistent, frame-indifferent model of large-strain thermoviscoelasticity using second-grade nonsimple materials, and proves the existence of weak solutions in a quasistatic setting.

## Contribution

It introduces a novel thermoviscoelastic model at large strains that ensures frame indifference and thermodynamic consistency, with a proof of weak solution existence.

## Key findings

- Model formulation in the reference configuration.
- Frame indifference of viscous and elastic stresses.
- Existence of weak solutions in quasistatic regime.

## Abstract

The frame-indifferent thermodynamically-consistent model of thermoviscoelasticity at large strain is formulated in the reference configuration with using the concept of the second-grade nonsimple materials. We focus on physically correct viscous stresses that are frame indifferent under time-dependent rotations. Also elastic stresses are frame indifferent under rotations and respect positivity of the determinant of the deformation gradient. The heat transfer is governed by the Fourier law in the actual deformed configuration, which leads to a nontrivial description when pulled back into the reference configuration. Existence of weak solutions in the quasistatic setting, i.e.\ inertial forces are ignored, is shown by time discretization.