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A first-order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme

Jibran Haider, Chun Hean Lee Orcid Logo, Antonio Gil Orcid Logo, Javier Bonet

International Journal for Numerical Methods in Engineering, Volume: 109, Issue: 3, Pages: 407 - 456

Swansea University Authors: Jibran Haider , Chun Hean Lee Orcid Logo, Antonio Gil Orcid Logo

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DOI (Published version): 10.1002/nme.5293

Abstract

This paper builds on recent work developed by the authors for the numerical analysis of large strain solid dynamics, by introducing an upwind cell centred hexahedral finite volume framework implemented within the open source code OpenFOAM [http://www.openfoam.com/]. In Lee, Gil and Bonet (2013), a f...

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Published in: International Journal for Numerical Methods in Engineering
ISSN: 0029-5981
Published: 2017
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URI: https://cronfa.swan.ac.uk/Record/cronfa27826
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spelling 2020-06-23T17:03:46.6265343 v2 27826 2016-05-12 A first-order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme 928fdeb0bcd8a40e5d3f08fe85989c7f Jibran Haider Jibran Haider true false e3024bdeee2dee48376c2a76b7147f2f 0000-0003-1102-3729 Chun Hean Lee Chun Hean Lee true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false 2016-05-12 EEN This paper builds on recent work developed by the authors for the numerical analysis of large strain solid dynamics, by introducing an upwind cell centred hexahedral finite volume framework implemented within the open source code OpenFOAM [http://www.openfoam.com/]. In Lee, Gil and Bonet (2013), a first-order hyperbolic system of conservation laws was introduced in terms of the linear momentum and the deformation gradient tensor of the system, leading to excellent behaviour in two-dimensional bending dominated nearly incompressible scenarios. The main aim of this paper is the extension of this algorithm into three dimensions, its tailor-made implementation into OpenFOAM and the enhancement of the formulation with three key novelties. First, the introduction of two different strategies in order to ensure the satisfaction of the underlying involutions of the system, that is, that the deformation gradient tensor must be curl-free throughout the deformation process. Second, the use of a discrete angular momentum projection algorithm and a monolithic Total Variation Diminishing Runge-Kutta time integrator combined in order to guarantee the conservation of angular momentum. Third, and for comparison purposes, an adapted Total Lagrangian version of the hyperelastic-GLACE nodal scheme of Kluth and Després (2010) is presented. A series of challenging numerical examples are examined in order to assess the robustness and accuracy of the proposed algorithm, benchmarking it against an ample spectrum of alternative numerical strategies developed by the authors in recent publications. Journal Article International Journal for Numerical Methods in Engineering 109 3 407 456 0029-5981 31 12 2017 2017-12-31 10.1002/nme.5293 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2020-06-23T17:03:46.6265343 2016-05-12T09:39:21.0988517 College of Engineering Engineering Jibran Haider 1 Chun Hean Lee 0000-0003-1102-3729 2 Antonio Gil 0000-0001-7753-1414 3 Javier Bonet 4 0027826-512201694216AM.pdf An_upwind_cell_centred_Total_Lagrangian_Scheme.pdf 2016-05-12T09:42:16.3030000 Output 19946098 application/pdf Accepted Manuscript true 2017-05-10T00:00:00.0000000 This is the peer reviewed version of the article which has been published in final form. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions. true eng https://authorservices.wiley.com/author-resources/Journal-Authors/licensing/self-archiving.html
title A first-order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme
spellingShingle A first-order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme
Jibran, Haider
Chun Hean, Lee
Antonio, Gil
title_short A first-order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme
title_full A first-order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme
title_fullStr A first-order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme
title_full_unstemmed A first-order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme
title_sort A first-order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme
author_id_str_mv 928fdeb0bcd8a40e5d3f08fe85989c7f
e3024bdeee2dee48376c2a76b7147f2f
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author_id_fullname_str_mv 928fdeb0bcd8a40e5d3f08fe85989c7f_***_Jibran, Haider_***_
e3024bdeee2dee48376c2a76b7147f2f_***_Chun Hean, Lee_***_0000-0003-1102-3729
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio, Gil_***_0000-0001-7753-1414
author Jibran, Haider
Chun Hean, Lee
Antonio, Gil
author2 Jibran Haider
Chun Hean Lee
Antonio Gil
Javier Bonet
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container_title International Journal for Numerical Methods in Engineering
container_volume 109
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publishDate 2017
institution Swansea University
issn 0029-5981
doi_str_mv 10.1002/nme.5293
college_str College of Engineering
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hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
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description This paper builds on recent work developed by the authors for the numerical analysis of large strain solid dynamics, by introducing an upwind cell centred hexahedral finite volume framework implemented within the open source code OpenFOAM [http://www.openfoam.com/]. In Lee, Gil and Bonet (2013), a first-order hyperbolic system of conservation laws was introduced in terms of the linear momentum and the deformation gradient tensor of the system, leading to excellent behaviour in two-dimensional bending dominated nearly incompressible scenarios. The main aim of this paper is the extension of this algorithm into three dimensions, its tailor-made implementation into OpenFOAM and the enhancement of the formulation with three key novelties. First, the introduction of two different strategies in order to ensure the satisfaction of the underlying involutions of the system, that is, that the deformation gradient tensor must be curl-free throughout the deformation process. Second, the use of a discrete angular momentum projection algorithm and a monolithic Total Variation Diminishing Runge-Kutta time integrator combined in order to guarantee the conservation of angular momentum. Third, and for comparison purposes, an adapted Total Lagrangian version of the hyperelastic-GLACE nodal scheme of Kluth and Després (2010) is presented. A series of challenging numerical examples are examined in order to assess the robustness and accuracy of the proposed algorithm, benchmarking it against an ample spectrum of alternative numerical strategies developed by the authors in recent publications.
published_date 2017-12-31T03:48:08Z
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