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A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes

Thomas Di Giusto, Chun Hean Lee, Antonio Gil Orcid Logo, Javier Bonet, Clare Wood Orcid Logo, Matteo Giacomini

Journal of Computational Physics, Volume: 518, Start page: 113322

Swansea University Authors: Thomas Di Giusto, Antonio Gil Orcid Logo, Clare Wood Orcid Logo

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DOI (Published version): 10.1016/j.jcp.2024.113322

Abstract

The paper introduces a computational framework that makes use of a novel Arbitrary Lagrangian Eulerian (ALE) conservation law formulation for nonlinear solid dynamics. In addition to the standard mass conservation law and the linear momentum conservation law, the framework extends its application to...

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Published in: Journal of Computational Physics
ISSN: 0021-9991
Published: Elsevier BV 2024
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URI: https://cronfa.swan.ac.uk/Record/cronfa67331
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To maintain equal convergence orders for all variables (strains/stresses, velocities/displacements and temperature/entropy), the standard deformation gradient tensor (measured from material to spatial configuration) is evaluated through a multiplicative decomposition into two auxiliary deformation gradient tensors. Both are obtained through additional first-order conservation laws. The exploitation of the hyperbolic nature of the underlying system, together with accurate wave speed bounds, ensures the stability of explicit time integrators. For spatial discretisation, a vertex-centred Godunov-type Finite Volume method is employed and suitably adapted to the formulation at hand. To guarantee stability from both the continuum and the semi-discretisation standpoints, a carefully designed numerical interface flux is presented. 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spelling v2 67331 2024-08-07 A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes cb063b1974c868e8dd66a345f6772be7 Thomas Di Giusto Thomas Di Giusto true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 97bede20cc14db118af8abfbb687e895 0000-0003-0001-0121 Clare Wood Clare Wood true false 2024-08-07 ACEM The paper introduces a computational framework that makes use of a novel Arbitrary Lagrangian Eulerian (ALE) conservation law formulation for nonlinear solid dynamics. In addition to the standard mass conservation law and the linear momentum conservation law, the framework extends its application to consider more general irreversible processes such as thermo-elasticity and thermo-visco-plasticity. This requires the incorporation of the first law of thermodynamics, expressed in terms of the entropy density, as an additional conservation law. To disassociate material particles from mesh positions, the framework introduces an additional reference configuration, extending beyond conventional material and spatial descriptions. The determination of the mesh motion involves the solution of a conservation-type momentum equation, ensuring optimal mesh movement and contributing to maintaining a high-quality mesh and improving solution accuracy, particularly in regions undergoing large plastic flows. To maintain equal convergence orders for all variables (strains/stresses, velocities/displacements and temperature/entropy), the standard deformation gradient tensor (measured from material to spatial configuration) is evaluated through a multiplicative decomposition into two auxiliary deformation gradient tensors. Both are obtained through additional first-order conservation laws. The exploitation of the hyperbolic nature of the underlying system, together with accurate wave speed bounds, ensures the stability of explicit time integrators. For spatial discretisation, a vertex-centred Godunov-type Finite Volume method is employed and suitably adapted to the formulation at hand. To guarantee stability from both the continuum and the semi-discretisation standpoints, a carefully designed numerical interface flux is presented. Lyapunov stability analysis is carried out by evaluating the time variation of the Ballistic energy of the system, aiming to ensure the positive production of numerical entropy. Finally, a variety of three dimensional benchmark problems are presented to illustrate the robustness and applicability of the framework. Journal Article Journal of Computational Physics 518 113322 Elsevier BV 0021-9991 Solid dynamics; Conservation laws; Arbitrary Lagrangian Eulerian; Ballistic; Large strain; Godunov-type finite volume method 1 12 2024 2024-12-01 10.1016/j.jcp.2024.113322 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM Swansea University SU Library paid the OA fee (TA Institutional Deal) The first, second and third authors would like to acknowledge the financial support received through the project Marie Skłodowska-Curie ITN-EJD ProTechTion, funded by the European Union Horizon 2020 research and innovation program with grant number 764636. CHL acknowledges the support provided by FIFTY2 Technology GmbH via project reference 322835. AJG acknowledges the support provided by UK AWE via project PO 40062030. JB acknowledges the financial support received via project POTENTIAL (PID2022-141957OB-C21) funded by MICIU/AEI/10.13039/501100011033/FEDER, UE. MG acknowledges the Spanish Ministry of Science, Innovation and Universities and Spanish State Research Agency MICIU/AEI/10.13039/501100011033 (Grants No. PID2020-113463RB-C33 and CEX2018-000797-S) and the Generalitat de Catalunya (Grant No. 2021-SGR-01049). MG is Fellow of the Serra Húnter Programme of the Generalitat de Catalunya. 2024-09-19T10:40:57.6982344 2024-08-07T10:21:37.5237635 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering Thomas Di Giusto 1 Chun Hean Lee 2 Antonio Gil 0000-0001-7753-1414 3 Javier Bonet 4 Clare Wood 0000-0003-0001-0121 5 Matteo Giacomini 6 67331__31371__474083f2c6474d9e88442d64be12b26c.pdf 67331.VoR.pdf 2024-09-19T10:38:43.5472661 Output 17601155 application/pdf Version of Record true © 2024 The Author(s). This is an open access article under the CC BY license. true eng http://creativecommons.org/licenses/by/4.0/).
title A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes
spellingShingle A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes
Thomas Di Giusto
Antonio Gil
Clare Wood
title_short A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes
title_full A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes
title_fullStr A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes
title_full_unstemmed A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes
title_sort A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for nonlinear solid dynamics in irreversible processes
author_id_str_mv cb063b1974c868e8dd66a345f6772be7
1f5666865d1c6de9469f8b7d0d6d30e2
97bede20cc14db118af8abfbb687e895
author_id_fullname_str_mv cb063b1974c868e8dd66a345f6772be7_***_Thomas Di Giusto
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
97bede20cc14db118af8abfbb687e895_***_Clare Wood
author Thomas Di Giusto
Antonio Gil
Clare Wood
author2 Thomas Di Giusto
Chun Hean Lee
Antonio Gil
Javier Bonet
Clare Wood
Matteo Giacomini
format Journal article
container_title Journal of Computational Physics
container_volume 518
container_start_page 113322
publishDate 2024
institution Swansea University
issn 0021-9991
doi_str_mv 10.1016/j.jcp.2024.113322
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 - Aerospace Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Aerospace Engineering
document_store_str 1
active_str 0
description The paper introduces a computational framework that makes use of a novel Arbitrary Lagrangian Eulerian (ALE) conservation law formulation for nonlinear solid dynamics. In addition to the standard mass conservation law and the linear momentum conservation law, the framework extends its application to consider more general irreversible processes such as thermo-elasticity and thermo-visco-plasticity. This requires the incorporation of the first law of thermodynamics, expressed in terms of the entropy density, as an additional conservation law. To disassociate material particles from mesh positions, the framework introduces an additional reference configuration, extending beyond conventional material and spatial descriptions. The determination of the mesh motion involves the solution of a conservation-type momentum equation, ensuring optimal mesh movement and contributing to maintaining a high-quality mesh and improving solution accuracy, particularly in regions undergoing large plastic flows. To maintain equal convergence orders for all variables (strains/stresses, velocities/displacements and temperature/entropy), the standard deformation gradient tensor (measured from material to spatial configuration) is evaluated through a multiplicative decomposition into two auxiliary deformation gradient tensors. Both are obtained through additional first-order conservation laws. The exploitation of the hyperbolic nature of the underlying system, together with accurate wave speed bounds, ensures the stability of explicit time integrators. For spatial discretisation, a vertex-centred Godunov-type Finite Volume method is employed and suitably adapted to the formulation at hand. To guarantee stability from both the continuum and the semi-discretisation standpoints, a carefully designed numerical interface flux is presented. Lyapunov stability analysis is carried out by evaluating the time variation of the Ballistic energy of the system, aiming to ensure the positive production of numerical entropy. Finally, a variety of three dimensional benchmark problems are presented to illustrate the robustness and applicability of the framework.
published_date 2024-12-01T10:40:57Z
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score 11.037581

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