Thermo-elastodynamics of finitely-strained multipolar viscous solids with an energy-controlled stress
Abstract
The thermodynamical model of viscoelastic deformable solids at finite strains with Kelvin-Voigt rheology with a higher-order viscosity (using the concept of multipolar materials) is formulated in a fully Eulerian way in rates. Assumptions used in this paper allow for a physically justified free energy leading to non-negative entropy that satisfies the 3rd law of thermodynamics, i.e. entropy vanishes at zero temperature, and energy-controlled stress. This last attribute is used advantageously to prove the existence and a certain regularity of weak solutions by a simplified Faedo-Galerkin semi-discretization, based on estimates obtained from the total-energy and the mechanical-energy balances. Some examples that model neo-Hookean-type materials are presented, too.
Keywords
Cite
@article{arxiv.2404.13188,
title = {Thermo-elastodynamics of finitely-strained multipolar viscous solids with an energy-controlled stress},
author = {Tomáš Roubíček},
journal= {arXiv preprint arXiv:2404.13188},
year = {2025}
}