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

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

International Journal for Numerical Methods in Engineering

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

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DOI (Published version): 10.1002/nme.7467

Abstract

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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Published in: International Journal for Numerical Methods in Engineering
Published: Wiley 2024
URI: https://cronfa.swan.ac.uk/Record/cronfa65812
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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 demonstratedvia the use of the time variation of the Hamiltonian of the system, seeking to ensure the positiveproduction of numerical entropy. A range of three dimensional benchmark problems will be presented in order to demonstrate the robustness and reliability of the framework. 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spelling v2 65812 2024-03-11 A first-order hyperbolic Arbitrary Lagrangian Eulerian conservation formulation for non-linear solid dynamics cb063b1974c868e8dd66a345f6772be7 Thomas Di Giusto Thomas Di Giusto true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2024-03-11 CIVL 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 demonstratedvia the use of the time variation of the Hamiltonian of the system, seeking to ensure the positiveproduction 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. Journal Article International Journal for Numerical Methods in Engineering 0 Wiley Fast dynamics, Conservation laws, Arbitrary Lagrangian Eulerian, Hamiltonian, Large strain, Finite volume method 24 4 2024 2024-04-24 10.1002/nme.7467 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University Another institution paid the OA fee European Union Horizon 2020. Grant Number: 764636; EPSRC. Grant Number: EP/R008531/1; K AWE. Grant Number: PO 40062030; MCIN. Grant Numbers: PID2020-113463RB-C33, PID2022-141957OB-C21, CEX2018-000797-S 2024-04-24T14:52:34.4724942 2024-03-11T12:45:52.0147240 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering Thomas Di Giusto 1 Antonio Gil 0000-0001-7753-1414 2 Chun Hean Lee 3 Javier Bonet 4 Matteo Giacomini 5 65812__30135__50c52779c9fc49d68582dafe58d94d82.pdf 65812.VoR.pdf 2024-04-24T14:48:02.8202515 Output 9865682 application/pdf Version of Record true © 2024 The Authors. This is an open access article under the terms of the Creative Commons Attribution License. true eng http://creativecommons.org/licenses/by/4.0/
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
Thomas Di Giusto
Antonio Gil
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
author_id_str_mv cb063b1974c868e8dd66a345f6772be7
1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv cb063b1974c868e8dd66a345f6772be7_***_Thomas Di Giusto
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
author Thomas Di Giusto
Antonio Gil
author2 Thomas Di Giusto
Antonio Gil
Chun Hean Lee
Javier Bonet
Matteo Giacomini
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 0
publishDate 2024
institution Swansea University
doi_str_mv 10.1002/nme.7467
publisher Wiley
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 - Mechanical Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Mechanical Engineering
document_store_str 1
active_str 0
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 demonstratedvia the use of the time variation of the Hamiltonian of the system, seeking to ensure the positiveproduction 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.
published_date 2024-04-24T14:52:33Z
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