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arXiv · 2203.06080

Thermodynamics of viscoelastic solids, its Eulerian formulation, and existence of weak solutions

Tomáš Roubíček
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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.

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Tomáš Roubíček. 2022-03-11. Thermodynamics of viscoelastic solids, its Eulerian formulation, and existence of weak solutions. https://arxiv.org/abs/2203.06080

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