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Finite strain thermoelasticity and the Third Law of thermodynamics

Javier Bonet Orcid Logo, Antonio Gil Orcid Logo

Journal of the Mechanics and Physics of Solids, Volume: 206, Issue: Part A, Start page: 106372

Swansea University Author: Antonio Gil Orcid Logo

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DOI (Published version): 10.1016/j.jmps.2025.106372

Abstract

This paper shows that commonly used large strain thermoelastic models in which the specific heat coefficient is constant or, at most, changes with temperature, are incompatible with the Third Law of thermodynamics, namely, that “entropy should be zero at the Kelvin state, that is, absolute zero temp...

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Published in: Journal of the Mechanics and Physics of Solids
ISSN: 0022-5096 1873-4782
Published: Elsevier BV 2026
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URI: https://cronfa.swan.ac.uk/Record/cronfa70443
first_indexed 2025-09-22T08:14:36Z
last_indexed 2025-10-24T18:37:37Z
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spelling 2025-10-23T16:14:14.2277943 v2 70443 2025-09-22 Finite strain thermoelasticity and the Third Law of thermodynamics 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2025-09-22 ACEM This paper shows that commonly used large strain thermoelastic models in which the specific heat coefficient is constant or, at most, changes with temperature, are incompatible with the Third Law of thermodynamics, namely, that “entropy should be zero at the Kelvin state, that is, absolute zero temperature”. In particular, it will be shown that the Third Law implies that the specific heat coefficient must vary with deformation for the coupling between mechanical and thermal effects to take place. In line with this result, a simple analytical constitutive model consistent with the Third Law will be proposed. The model will be based on a multiplicative decomposition of the specific heat into a deformation dependent part and a temperature dependent component. The resulting thermoelastic model complies with the Third Law and, in addition, the necessary convexity conditions that ensure the existence of real wave speeds. It can replicate existing entropic elasticity models for rubber, describe melting and softening behaviour, and converge to the classical relationships for linear thermoelasticity in the small strain regime. Journal Article Journal of the Mechanics and Physics of Solids 206 Part A 106372 Elsevier BV 0022-5096 1873-4782 Third Law of thermodynamics; Finite strains; Thermoelasticity; Specific heat coefficient; Polyconvexity; Free energy potential 1 1 2026 2026-01-01 10.1016/j.jmps.2025.106372 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University SU Library paid the OA fee (TA Institutional Deal) The authors acknowledge funding received from grants PID2022-141957OB-C21 and PID2022-141957OA-C22 financed by MCIN/AEI /10.13039/501100011033/ FEDER, UE. A. J. Gil wishes to acknowledge the support provided by the Defence, Science and Technology Laboratory (Dstl) and The Leverhulme Trust Foundation (UK) through a Leverhulme Fellowship . 2025-10-23T16:14:14.2277943 2025-09-22T09:10:16.2739664 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Javier Bonet 0000-0002-0430-5181 1 Antonio Gil 0000-0001-7753-1414 2 70443__35461__aa77d4ad41994ab8a84075085a597ebc.pdf 70443.VOR.pdf 2025-10-23T16:09:02.2035471 Output 1351452 application/pdf Version of Record true © 2025 The Authors. This is an open access article distributed under the terms of the Creative Commons CC-BY license. true eng http://creativecommons.org/licenses/by/4.0/
title Finite strain thermoelasticity and the Third Law of thermodynamics
spellingShingle Finite strain thermoelasticity and the Third Law of thermodynamics
Antonio Gil
title_short Finite strain thermoelasticity and the Third Law of thermodynamics
title_full Finite strain thermoelasticity and the Third Law of thermodynamics
title_fullStr Finite strain thermoelasticity and the Third Law of thermodynamics
title_full_unstemmed Finite strain thermoelasticity and the Third Law of thermodynamics
title_sort Finite strain thermoelasticity and the Third Law of thermodynamics
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Antonio Gil
author2 Javier Bonet
Antonio Gil
format Journal article
container_title Journal of the Mechanics and Physics of Solids
container_volume 206
container_issue Part A
container_start_page 106372
publishDate 2026
institution Swansea University
issn 0022-5096
1873-4782
doi_str_mv 10.1016/j.jmps.2025.106372
publisher Elsevier BV
college_str Faculty of Science and Engineering
hierarchytype
hierarchy_top_id facultyofscienceandengineering
hierarchy_top_title Faculty of Science and Engineering
hierarchy_parent_id facultyofscienceandengineering
hierarchy_parent_title Faculty of Science and Engineering
department_str School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
document_store_str 1
active_str 0
description This paper shows that commonly used large strain thermoelastic models in which the specific heat coefficient is constant or, at most, changes with temperature, are incompatible with the Third Law of thermodynamics, namely, that “entropy should be zero at the Kelvin state, that is, absolute zero temperature”. In particular, it will be shown that the Third Law implies that the specific heat coefficient must vary with deformation for the coupling between mechanical and thermal effects to take place. In line with this result, a simple analytical constitutive model consistent with the Third Law will be proposed. The model will be based on a multiplicative decomposition of the specific heat into a deformation dependent part and a temperature dependent component. The resulting thermoelastic model complies with the Third Law and, in addition, the necessary convexity conditions that ensure the existence of real wave speeds. It can replicate existing entropic elasticity models for rubber, describe melting and softening behaviour, and converge to the classical relationships for linear thermoelasticity in the small strain regime.
published_date 2026-01-01T05:32:44Z
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score 11.096295

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