Thermodynamics of viscoelastic solids, its Eulerian formulation, and existence of weak solutions
Abstract
The thermodynamical model of visco-elastic deformable solids at finite strains is formulated in a fully Eulerian way in rates. Also effects of thermal expansion or buoyancy due to evolving mass density in a gravity field are covered. The Kelvin-Voigt rheology with a higher-order viscosity (exploiting the concept of multipolar materials) is used, allowing for physically relevant frame-indifferent stored energies and for local invertibility of deformation. The model complies with energy conservation and Clausius-Duhem entropy inequality. Existence and a certain regularity of weak solutions is proved by a Faedo-Galerkin semi-discretization and a suitable regularization. Subtle physical limitations of the model are illustrated on thermally expanding neo-Hookean materials or materials with phase transitions.
Keywords
Cite
@article{arxiv.2203.06080,
title = {Thermodynamics of viscoelastic solids, its Eulerian formulation, and existence of weak solutions},
author = {Tomáš Roubíček},
journal= {arXiv preprint arXiv:2203.06080},
year = {2023}
}