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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; Antonio J. Gil; Javier Bonet

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

Swansea University Author: Gil, Antonio

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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/cronfa28512
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spelling 2018-01-19T15:22:35Z v2 28512 2016-06-03 A first-order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme Antonio Gil Antonio Gil true 0000-0001-7753-1414 false 1f5666865d1c6de9469f8b7d0d6d30e2 d66249f916a874bda4f708760a8d2027 Gy3Cg4qrL2LY4pTET3406oJSbZF11mHm1K8NtCGVMYw= 2016-06-03 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 0 0 2017 2017-01-01 10.1002/nme.5293 College of Engineering Engineering CENG EEN None None 2018-01-19T15:22:35Z 2016-06-03T12:13:23Z College of Engineering Engineering Jibran Haider 1 Chun Hean Lee 2 Antonio J. Gil 3 Javier Bonet 4 0028512-29072016142443.pdf haider2016.pdf 2016-07-29T14:24:43Z Output 13982527 application/pdf AM true Published to Cronfa 29/07/2016 2017-05-10T00:00:00 false
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
Gil, Antonio
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 1f5666865d1c6de9469f8b7d0d6d30e2
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Gil, Antonio
author Gil, Antonio
author2 Jibran Haider
Chun Hean Lee
Antonio J. Gil
Javier Bonet
format Journal article
container_title International Journal for Numerical Methods in Engineering
container_volume 109
container_issue 3
container_start_page 407
publishDate 2017
institution Swansea University
issn 0029-5981
doi_str_mv 10.1002/nme.5293
college_str College of Engineering
hierarchytype
hierarchy_top_id collegeofengineering
hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
document_store_str 1
active_str 1
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 2017-01-01T21:38:34Z
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