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An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity

Ataollah Ghavamian, Chun Hean Lee, Antonio Gil Orcid Logo, Javier Bonet, Thomas Heuzé, Laurent Stainier

Computer Methods in Applied Mechanics and Engineering, Volume: 379, Start page: 113736

Swansea University Authors: Ataollah Ghavamian , Antonio Gil Orcid Logo

  • Accepted Manuscript under embargo until: 9th March 2022

Abstract

This paper presents a novel Smooth Particle Hydrodynamics computational framework for the simulation of large strain fast solid dynamics in thermo-elasticity. The formulation is based on the Total Lagrangian description of a system of first order conservation laws written in terms of the linear mome...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: Elsevier BV 2021
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URI: https://cronfa.swan.ac.uk/Record/cronfa56268
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spelling 2021-05-28T18:53:22.0761378 v2 56268 2021-02-16 An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity ea56d8e69b28541a1b2c201f7dc0b6d4 Ataollah Ghavamian Ataollah Ghavamian true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2021-02-16 EEN This paper presents a novel Smooth Particle Hydrodynamics computational framework for the simulation of large strain fast solid dynamics in thermo-elasticity. The formulation is based on the Total Lagrangian description of a system of first order conservation laws written in terms of the linear momentum, the triplet of deformation measures (also known as minors of the deformation gradient tensor) and the total energy of the system, extending thus the previous work carried out by some of the authors in the context of isothermal elasticity and elasto-plasticity (Lee et al., 2016; Lee et al., 2017; Lee et al., 2019). To ensure the stability (i.e. hyperbolicity) of the formulation from the continuum point of view, the internal energy density is expressed as a polyconvex combination of the triplet of deformation measures and the entropy density. Moreover, and to guarantee stability from the spatial discretisation point of view, consistently derived Riemann-based numerical dissipation is carefully introduced where local numerical entropy production is demonstrated via a novel technique in terms of the time rate of the so-called ballistic free energy of the system. For completeness, an alternative and equally competitive formulation (in the case of smooth solutions), expressed in terms of the entropy density, is also implemented and compared. A series of numerical examples is presented in order to assess the applicability and robustness of the proposed formulations, where the Smooth Particle Hydrodynamics scheme is benchmarked against an alternative in-house Finite Volume Vertex Centred implementation. Journal Article Computer Methods in Applied Mechanics and Engineering 379 113736 Elsevier BV 0045-7825 Conservation laws, SPH, Upwind, Riemann Solver, Explicit dynamics, Thermo-elasticity 1 6 2021 2021-06-01 10.1016/j.cma.2021.113736 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2021-05-28T18:53:22.0761378 2021-02-16T16:18:33.9369585 College of Engineering Engineering Ataollah Ghavamian 1 Chun Hean Lee 2 Antonio Gil 0000-0001-7753-1414 3 Javier Bonet 4 Thomas Heuzé 5 Laurent Stainier 6 Under embargo Under embargo 2021-02-16T16:23:26.1536513 Output 38276285 application/pdf Accepted Manuscript true 2022-03-09T00:00:00.0000000 ©2021 All rights reserved. All article content, except where otherwise noted, is licensed under a Creative Commons Attribution Non-Commercial No Derivatives License (CC-BY-NC-ND) true eng http://creativecommons.org/licenses/by-nc-nd/4.0/
title An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity
spellingShingle An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity
Ataollah, Ghavamian
Antonio, Gil
title_short An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity
title_full An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity
title_fullStr An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity
title_full_unstemmed An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity
title_sort An entropy-stable Smooth Particle Hydrodynamics algorithm for large strain thermo-elasticity
author_id_str_mv ea56d8e69b28541a1b2c201f7dc0b6d4
1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv ea56d8e69b28541a1b2c201f7dc0b6d4_***_Ataollah, Ghavamian_***_
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio, Gil_***_0000-0001-7753-1414
author Ataollah, Ghavamian
Antonio, Gil
author2 Ataollah Ghavamian
Chun Hean Lee
Antonio Gil
Javier Bonet
Thomas Heuzé
Laurent Stainier
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 379
container_start_page 113736
publishDate 2021
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2021.113736
publisher Elsevier BV
college_str College of Engineering
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hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
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description This paper presents a novel Smooth Particle Hydrodynamics computational framework for the simulation of large strain fast solid dynamics in thermo-elasticity. The formulation is based on the Total Lagrangian description of a system of first order conservation laws written in terms of the linear momentum, the triplet of deformation measures (also known as minors of the deformation gradient tensor) and the total energy of the system, extending thus the previous work carried out by some of the authors in the context of isothermal elasticity and elasto-plasticity (Lee et al., 2016; Lee et al., 2017; Lee et al., 2019). To ensure the stability (i.e. hyperbolicity) of the formulation from the continuum point of view, the internal energy density is expressed as a polyconvex combination of the triplet of deformation measures and the entropy density. Moreover, and to guarantee stability from the spatial discretisation point of view, consistently derived Riemann-based numerical dissipation is carefully introduced where local numerical entropy production is demonstrated via a novel technique in terms of the time rate of the so-called ballistic free energy of the system. For completeness, an alternative and equally competitive formulation (in the case of smooth solutions), expressed in terms of the entropy density, is also implemented and compared. A series of numerical examples is presented in order to assess the applicability and robustness of the proposed formulations, where the Smooth Particle Hydrodynamics scheme is benchmarked against an alternative in-house Finite Volume Vertex Centred implementation.
published_date 2021-06-01T04:24:25Z
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