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

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

doi:10.1002/nme.7467

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

Thomas Di Giusto, Antonio Gil

, Chun Hean Lee, Javier Bonet, Matteo Giacomini

International Journal for Numerical Methods in Engineering, Volume: 125, Issue: 15

Swansea University Authors: Thomas Di Giusto, Antonio Gil

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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
ISSN:	0029-5981 1097-0207
Published:	Wiley 2024
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URI:	https://cronfa.swan.ac.uk/Record/cronfa65812
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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 ACEM 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 125 15 Wiley 0029-5981 1097-0207 Arbitrary Lagrangian Eulerian, conservation laws, fast dynamics, Hamiltonian, large strain, finite volume method 19 7 2024 2024-07-19 10.1002/nme.7467 COLLEGE NANME Aerospace, Civil, Electrical, and Mechanical Engineering COLLEGE CODE ACEM 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 2024-10-08T11:44:26.2931094 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	125
container_issue	15
publishDate	2024
institution	Swansea University
issn	0029-5981 1097-0207
doi_str_mv	10.1002/nme.7467
publisher	Wiley
college_str	Faculty of Science and Engineering
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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
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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	2024-07-19T11:44:24Z
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score	11.036706

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

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