A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics

The paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first-order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in orde...

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Autores: Giusto, Thomas di, Chun Hean, Lee, Antonio Javier, Gil, Bonet Carbonell, Javier|||0000-0002-0430-5181, Giacomini, Matteo|||0000-0001-6094-5944
Tipo de recurso: artículo
Fecha de publicación:2024
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/420799
Acceso en línea:https://hdl.handle.net/2117/420799
https://dx.doi.org/10.1002/nme.7467
Access Level:acceso abierto
Palabra clave:Arbitrary Lagrangian Eulerian
Conservation laws
Fast dynamics
Hamiltonian
Large strain
Finitevolume method
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
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dc.title.none.fl_str_mv A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics
title A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics
spellingShingle A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics
Giusto, Thomas di
Arbitrary Lagrangian Eulerian
Conservation laws
Fast dynamics
Hamiltonian
Large strain
Finitevolume method
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
title_short A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics
title_full A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics
title_fullStr A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics
title_full_unstemmed A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics
title_sort A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics
dc.creator.none.fl_str_mv Giusto, Thomas di
Chun Hean, Lee
Antonio Javier, Gil
Bonet Carbonell, Javier|||0000-0002-0430-5181
Giacomini, Matteo|||0000-0001-6094-5944
author Giusto, Thomas di
author_facet Giusto, Thomas di
Chun Hean, Lee
Antonio Javier, Gil
Bonet Carbonell, Javier|||0000-0002-0430-5181
Giacomini, Matteo|||0000-0001-6094-5944
author_role author
author2 Chun Hean, Lee
Antonio Javier, Gil
Bonet Carbonell, Javier|||0000-0002-0430-5181
Giacomini, Matteo|||0000-0001-6094-5944
author2_role author
author
author
author
dc.subject.none.fl_str_mv Arbitrary Lagrangian Eulerian
Conservation laws
Fast dynamics
Hamiltonian
Large strain
Finitevolume method
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
topic Arbitrary Lagrangian Eulerian
Conservation laws
Fast dynamics
Hamiltonian
Large strain
Finitevolume method
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
description The paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first-order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first-order conservation laws. Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. For spatial discretisation, a vertex-based Finite Volume method is employed and suitably adapted. To guarantee stability from both the continuum and the semi-discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstrated via the use of the time variation of the Hamiltonian of the system, seeking to ensure the positive production of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. Examples will be restricted to the case of isothermal reversible elasticity to demonstrate the potential of the new formulation.
publishDate 2024
dc.date.none.fl_str_mv 2024
2024-08-15
2024
2024-12-17
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/420799
https://dx.doi.org/10.1002/nme.7467
url https://hdl.handle.net/2117/420799
https://dx.doi.org/10.1002/nme.7467
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 764636 Industrial decision-making on complex production technologies supported by simulation-based engineering
Agencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113463RB-C33 MACHINE LEARNING FOR DATA-DRIVEN MODELING
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution 4.0 International
http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv John Wiley & sons
publisher.none.fl_str_mv John Wiley & sons
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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spelling A first-order hyperbolic arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamicsGiusto, Thomas diChun Hean, LeeAntonio Javier, GilBonet Carbonell, Javier|||0000-0002-0430-5181Giacomini, Matteo|||0000-0001-6094-5944Arbitrary Lagrangian EulerianConservation lawsFast dynamicsHamiltonianLarge strainFinitevolume methodÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèricaThe paper introduces a computational framework using a novel Arbitrary Lagrangian Eulerian (ALE) formalism in the form of a system of first-order conservation laws. In addition to the usual material and spatial configurations, an additional referential (intrinsic) configuration is introduced in order to disassociate material particles from mesh positions. Using isothermal hyperelasticity as a starting point, mass, linear momentum and total energy conservation equations are written and solved with respect to the reference configuration. In addition, with the purpose of guaranteeing equal order of convergence of strains/stresses and velocities/displacements, the computation of the standard deformation gradient tensor (measured from material to spatial configuration) is obtained via its multiplicative decomposition into two auxiliary deformation gradient tensors, both computed via additional first-order conservation laws. Crucially, the new ALE conservative formulation will be shown to degenerate elegantly into alternative mixed systems of conservation laws such as Total Lagrangian, Eulerian and Updated Reference Lagrangian. Hyperbolicity of the system of conservation laws will be shown and the accurate wave speed bounds will be presented, the latter critical to ensure stability of explicit time integrators. For spatial discretisation, a vertex-based Finite Volume method is employed and suitably adapted. To guarantee stability from both the continuum and the semi-discretisation standpoints, an appropriate numerical interface flux (by means of the Rankine–Hugoniot jump conditions) is carefully designed and presented. Stability is demonstrated via the use of the time variation of the Hamiltonian of the system, seeking to ensure the positive production of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. Examples will be restricted to the case of isothermal reversible elasticity to demonstrate the potential of the new formulation.The first, second and third authors would like to acknowledge the financial support received through the project MarieSkłodowska-Curie ITN-EJD ProTechTion, funded by the European Union Horizon 2020 research and innovation programwith grant number 764636. Chun Hean Lee acknowledges the support provided by the EPSRC Strategic Support Package:Engineering of Active Materials by Multiscale/Multiphysics Computational Mechanics–EP/R008531/1. Antonio J. Gilacknowledges the support provided by UK AWE via project PO 40062030. Javier Bonet acknowledges the financial supportreceived via project POTENTIAL (PID2022-141957OB-C21) funded by MCIN/AEI/10.13039/501100011033/FEDER, UE.Matteo Giacomini acknowledges the Spanish Ministry of Science and Innovation and Spanish State Research AgencyMCIN/AEI/10.13039/501100011033 (Grant nos. PID2020-113463RB-C33 and CEX2018-000797-S). Matteo Giacomini isFellow of the Serra Húnter Programme of the Generalitat de Catalunya.Peer ReviewedJohn Wiley & sons20242024-08-1520242024-12-17journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/420799https://dx.doi.org/10.1002/nme.7467reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)InglésengEuropean Commission http://doi.org/10.13039/100010661 Horizon 2020 Framework Programme 764636 Industrial decision-making on complex production technologies supported by simulation-based engineeringAgencia Estatal de Investigación http://doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020 PID2020-113463RB-C33 MACHINE LEARNING FOR DATA-DRIVEN MODELINGopen accesshttp://purl.org/coar/access_right/c_abf2Attribution 4.0 Internationalhttp://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4207992026-05-27T15:37:01Z
score 15.811543

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