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Symmetrisation and hyperbolicity of first-order conservation laws in large strain compressible viscoelasticity using the smoothed particle hydrodynamics method

Chun Hean Lee Orcid Logo, Antonio Gil Orcid Logo, Tadas Jaugielavičius, Thomas Richardson, Sébastien Boyaval Orcid Logo, Damien Violeau Orcid Logo, Javier Bonet Orcid Logo

Computer Methods in Applied Mechanics and Engineering, Volume: 452, Issue: Part B, Start page: 118742

Swansea University Authors: Antonio Gil Orcid Logo, Thomas Richardson

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DOI (Published version): 10.1016/j.cma.2026.118742

Abstract

This paper presents a new first-order hyperbolic framework with relaxation (or dissipation) terms for large strain viscoelastic solids. The framework is based on a compressible Maxwell-type viscoelastic model and integrates linear momentum conservation, geometric conservation laws, and evolution equ...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825 1879-2138
Published: Elsevier BV 2026
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URI: https://cronfa.swan.ac.uk/Record/cronfa71236
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spelling 2026-02-06T16:12:04.4352080 v2 71236 2026-01-13 Symmetrisation and hyperbolicity of first-order conservation laws in large strain compressible viscoelasticity using the smoothed particle hydrodynamics method 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false bf6476ea99a3a77ccc708c1da01b710f Thomas Richardson Thomas Richardson true false 2026-01-13 ACEM This paper presents a new first-order hyperbolic framework with relaxation (or dissipation) terms for large strain viscoelastic solids. The framework is based on a compressible Maxwell-type viscoelastic model and integrates linear momentum conservation, geometric conservation laws, and evolution equations for internal variables. First, we propose a polyconvex strain energy function that is jointly convex with respect to the deformation measures and internal variables. Second, we introduce a generalised convex entropy function to symmetrise the hyperbolic system in terms of dual conjugate (entropy) variables. Third, we demonstrate that the system is hyperbolic (i.e., real wave speeds) under all deformation states, and that the relaxation terms correctly capture viscoelastic dissipation. Fourth, we present an upwinding Smoothed Particle Hydrodynamics (SPH) [1–3] scheme that enforces the second law of thermodynamics semi-discretely and uses the time rate of the generalised convex entropy to monitor internal dissipation and stabilise the simulation. Finally, the proposed framework is validated through numerical examples and benchmarked against the in-house Updated Reference Lagragian SPH [2,3] and vertex-centred finite volume [4–7] algorithms, demonstrating stability, accuracy, and consistent energy dissipation. Journal Article Computer Methods in Applied Mechanics and Engineering 452 Part B 118742 Elsevier BV 0045-7825 1879-2138 Solid dynamics; Conservation laws; Smoothed particle hydrodynamic; Viscoelasticity; Riemann solver; Large strain 1 4 2026 2026-04-01 10.1016/j.cma.2026.118742 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University Another institution paid the OA fee CHL and TJ acknowledge support provided by FIFTY2 Technology GmbH (project 322835), AJG and TR from UK AWE (project PO 40062030), and JB from project POTENTIAL (PID2022-141957OB-C21) funded by MCIN/AEI/10.13039/501100011033/FEDER, UE. AJG also acknowledges support from The Leverhulme Trust Fellowship, and CHL acknowledges support from the RSE Personal Research Fellowship. FIFTY2 Technology GmbH (project 322835) UK AWE (project PO 40062030) Spain project POTENTIAL PID2022-141957OB-C21 2026-02-06T16:12:04.4352080 2026-01-13T13:05:05.0097356 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Chun Hean Lee 0000-0003-1102-3729 1 Antonio Gil 0000-0001-7753-1414 2 Tadas Jaugielavičius 3 Thomas Richardson 4 Sébastien Boyaval 0000-0002-7813-5146 5 Damien Violeau 0000-0002-2213-5251 6 Javier Bonet 0000-0002-0430-5181 7 71236__36207__95c2801739404e468842e7da80da730d.pdf 71236.VOR.pdf 2026-02-06T16:10:10.6936040 Output 41611120 application/pdf Version of Record true © 2026 The Author(s). 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 Symmetrisation and hyperbolicity of first-order conservation laws in large strain compressible viscoelasticity using the smoothed particle hydrodynamics method
spellingShingle Symmetrisation and hyperbolicity of first-order conservation laws in large strain compressible viscoelasticity using the smoothed particle hydrodynamics method
Antonio Gil
Thomas Richardson
title_short Symmetrisation and hyperbolicity of first-order conservation laws in large strain compressible viscoelasticity using the smoothed particle hydrodynamics method
title_full Symmetrisation and hyperbolicity of first-order conservation laws in large strain compressible viscoelasticity using the smoothed particle hydrodynamics method
title_fullStr Symmetrisation and hyperbolicity of first-order conservation laws in large strain compressible viscoelasticity using the smoothed particle hydrodynamics method
title_full_unstemmed Symmetrisation and hyperbolicity of first-order conservation laws in large strain compressible viscoelasticity using the smoothed particle hydrodynamics method
title_sort Symmetrisation and hyperbolicity of first-order conservation laws in large strain compressible viscoelasticity using the smoothed particle hydrodynamics method
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
bf6476ea99a3a77ccc708c1da01b710f
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
bf6476ea99a3a77ccc708c1da01b710f_***_Thomas Richardson
author Antonio Gil
Thomas Richardson
author2 Chun Hean Lee
Antonio Gil
Tadas Jaugielavičius
Thomas Richardson
Sébastien Boyaval
Damien Violeau
Javier Bonet
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 452
container_issue Part B
container_start_page 118742
publishDate 2026
institution Swansea University
issn 0045-7825
1879-2138
doi_str_mv 10.1016/j.cma.2026.118742
publisher Elsevier BV
college_str Faculty of Science and Engineering
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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 presents a new first-order hyperbolic framework with relaxation (or dissipation) terms for large strain viscoelastic solids. The framework is based on a compressible Maxwell-type viscoelastic model and integrates linear momentum conservation, geometric conservation laws, and evolution equations for internal variables. First, we propose a polyconvex strain energy function that is jointly convex with respect to the deformation measures and internal variables. Second, we introduce a generalised convex entropy function to symmetrise the hyperbolic system in terms of dual conjugate (entropy) variables. Third, we demonstrate that the system is hyperbolic (i.e., real wave speeds) under all deformation states, and that the relaxation terms correctly capture viscoelastic dissipation. Fourth, we present an upwinding Smoothed Particle Hydrodynamics (SPH) [1–3] scheme that enforces the second law of thermodynamics semi-discretely and uses the time rate of the generalised convex entropy to monitor internal dissipation and stabilise the simulation. Finally, the proposed framework is validated through numerical examples and benchmarked against the in-house Updated Reference Lagragian SPH [2,3] and vertex-centred finite volume [4–7] algorithms, demonstrating stability, accuracy, and consistent energy dissipation.
published_date 2026-04-01T05:34:48Z
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score 11.096068

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