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An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications

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

Computer Methods in Applied Mechanics and Engineering, Volume: 340, Pages: 684 - 727

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

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DOI (Published version): 10.1016/j.cma.2018.06.010

Abstract

The paper presents a new computational framework for the numerical simulation of fast large strain solid dynamics, with particular emphasis on the treatment of near incompressibility. A complete set of first order hyperbolic conservation equations expressed in terms of the linear momentum and the mi...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 00457825
Published: 2018
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URI: https://cronfa.swan.ac.uk/Record/cronfa40728
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A complete set of first order hyperbolic conservation equations expressed in terms of the linear momentum and the minors of the deformation (namely the deformation gradient, its co-factor and its Jacobian), in conjunction with a polyconvex nearly incompressible constitutive law, is presented. Taking advantage of this elegant formalism, alternative implementations in terms of entropy-conjugate variables are also possible, through suitable symmetrisation of the original system of conservation variables. From the spatial discretisation standpoint, modern Computational Fluid Dynamics code &#x201C;OpenFOAM&#x201D; [http://www.openfoam.com/] is here adapted to the field of solid mechanics, with the aim to bridge the gap between computational fluid and solid dynamics. A cell centred finite volume algorithm is employed and suitably adapted. Naturally, discontinuity of the conservation variables across control volume interfaces leads to a Riemann problem, whose resolution requires special attention when attempting to model materials with predominant nearly incompressible behaviour (&#x3BA;&#x2215;&#x3BC;&#x2265;500). For this reason, an acoustic Riemann solver combined with a preconditioning procedure is introduced. In addition, a global a posteriori angular momentum projection procedure proposed in Haider et al. (2017) is also presented and adapted to a Total Lagrangian version of the nodal scheme of Kluth and Despr&#xE9;s (2010) used in this paper for comparison purposes. 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spelling 2018-09-04T14:36:33.8081373 v2 40728 2018-06-18 An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications 928fdeb0bcd8a40e5d3f08fe85989c7f Jibran Haider Jibran Haider true false 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false e3024bdeee2dee48376c2a76b7147f2f 0000-0003-1102-3729 Chun Hean Lee Chun Hean Lee true false 2018-06-18 EEN The paper presents a new computational framework for the numerical simulation of fast large strain solid dynamics, with particular emphasis on the treatment of near incompressibility. A complete set of first order hyperbolic conservation equations expressed in terms of the linear momentum and the minors of the deformation (namely the deformation gradient, its co-factor and its Jacobian), in conjunction with a polyconvex nearly incompressible constitutive law, is presented. Taking advantage of this elegant formalism, alternative implementations in terms of entropy-conjugate variables are also possible, through suitable symmetrisation of the original system of conservation variables. From the spatial discretisation standpoint, modern Computational Fluid Dynamics code “OpenFOAM” [http://www.openfoam.com/] is here adapted to the field of solid mechanics, with the aim to bridge the gap between computational fluid and solid dynamics. A cell centred finite volume algorithm is employed and suitably adapted. Naturally, discontinuity of the conservation variables across control volume interfaces leads to a Riemann problem, whose resolution requires special attention when attempting to model materials with predominant nearly incompressible behaviour (κ∕μ≥500). For this reason, an acoustic Riemann solver combined with a preconditioning procedure is introduced. In addition, a global a posteriori angular momentum projection procedure proposed in Haider et al. (2017) is also presented and adapted to a Total Lagrangian version of the nodal scheme of Kluth and Després (2010) used in this paper for comparison purposes. Finally, a series of challenging numerical examples is examined in order to assess the robustness and applicability of the proposed methodology with an eye on large scale simulation in future works. Journal Article Computer Methods in Applied Mechanics and Engineering 340 684 727 00457825 First order conservation laws; Large strain solid dynamics; Finite volume method; Riemann solver; OpenFOAM 31 12 2018 2018-12-31 10.1016/j.cma.2018.06.010 COLLEGE NANME Engineering COLLEGE CODE EEN Swansea University 2018-09-04T14:36:33.8081373 2018-06-18T09:45:39.6298936 Faculty of Science and Engineering School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering Jibran Haider 1 Chun Hean Lee 2 Antonio Gil 0000-0001-7753-1414 3 Antonio Huerta 4 Javier Bonet 5 Chun Hean Lee 0000-0003-1102-3729 6 0040728-29062018113526.pdf haider2018(2).pdf 2018-06-29T11:35:26.5070000 Output 26287033 application/pdf Accepted Manuscript true 2019-06-25T00:00:00.0000000 true eng
title An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications
spellingShingle An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications
Jibran Haider
Antonio Gil
Chun Hean Lee
title_short An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications
title_full An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications
title_fullStr An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications
title_full_unstemmed An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications
title_sort An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications
author_id_str_mv 928fdeb0bcd8a40e5d3f08fe85989c7f
1f5666865d1c6de9469f8b7d0d6d30e2
e3024bdeee2dee48376c2a76b7147f2f
author_id_fullname_str_mv 928fdeb0bcd8a40e5d3f08fe85989c7f_***_Jibran Haider
1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
e3024bdeee2dee48376c2a76b7147f2f_***_Chun Hean Lee
author Jibran Haider
Antonio Gil
Chun Hean Lee
author2 Jibran Haider
Chun Hean Lee
Antonio Gil
Antonio Huerta
Javier Bonet
Chun Hean Lee
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 340
container_start_page 684
publishDate 2018
institution Swansea University
issn 00457825
doi_str_mv 10.1016/j.cma.2018.06.010
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 - Civil Engineering{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Aerospace, Civil, Electrical, General and Mechanical Engineering - Civil Engineering
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description The paper presents a new computational framework for the numerical simulation of fast large strain solid dynamics, with particular emphasis on the treatment of near incompressibility. A complete set of first order hyperbolic conservation equations expressed in terms of the linear momentum and the minors of the deformation (namely the deformation gradient, its co-factor and its Jacobian), in conjunction with a polyconvex nearly incompressible constitutive law, is presented. Taking advantage of this elegant formalism, alternative implementations in terms of entropy-conjugate variables are also possible, through suitable symmetrisation of the original system of conservation variables. From the spatial discretisation standpoint, modern Computational Fluid Dynamics code “OpenFOAM” [http://www.openfoam.com/] is here adapted to the field of solid mechanics, with the aim to bridge the gap between computational fluid and solid dynamics. A cell centred finite volume algorithm is employed and suitably adapted. Naturally, discontinuity of the conservation variables across control volume interfaces leads to a Riemann problem, whose resolution requires special attention when attempting to model materials with predominant nearly incompressible behaviour (κ∕μ≥500). For this reason, an acoustic Riemann solver combined with a preconditioning procedure is introduced. In addition, a global a posteriori angular momentum projection procedure proposed in Haider et al. (2017) is also presented and adapted to a Total Lagrangian version of the nodal scheme of Kluth and Després (2010) used in this paper for comparison purposes. Finally, a series of challenging numerical examples is examined in order to assess the robustness and applicability of the proposed methodology with an eye on large scale simulation in future works.
published_date 2018-12-31T03:51:51Z
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score 11.036706

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