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

Author:

Tomáš RoubíčekAuthors Info & Claims

Zeitschrift für angewandte Mathematik und Physik, Volume 75, Issue 2

https://doi.org/10.1007/s00033-023-02175-7

Published: 27 February 2024 Publication History

Abstract

The thermodynamic model of viscoelastic 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 are 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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Cited By

Mielke ARoubíček T(2025)A general thermodynamical model for finitely-strained continuum with inelasticity and diffusion, its GENERIC derivation in Eulerian formulation, and some applicationZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-024-02391-976:1Online publication date: 1-Feb-2025
https://dl.acm.org/doi/10.1007/s00033-024-02391-9

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cover image Zeitschrift für Angewandte Mathematik und Physik (ZAMP)

Zeitschrift für Angewandte Mathematik und Physik (ZAMP) Volume 75, Issue 2

Apr 2024

953 pages

Issue’s Table of Contents

© The Author(s), under exclusive licence to Springer Nature Switzerland AG 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

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Birkhauser Verlag

Switzerland

Publication History

Published: 27 February 2024

Accepted: 21 December 2023

Revision received: 16 December 2023

Received: 12 September 2023

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Cited By

Mielke ARoubíček T(2025)A general thermodynamical model for finitely-strained continuum with inelasticity and diffusion, its GENERIC derivation in Eulerian formulation, and some applicationZeitschrift für Angewandte Mathematik und Physik (ZAMP)10.1007/s00033-024-02391-976:1Online publication date: 1-Feb-2025
https://dl.acm.org/doi/10.1007/s00033-024-02391-9

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