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A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics

Antonio Gil Orcid Logo, Chun Hean Lee Orcid Logo, Javier Bonet Orcid Logo, Miquel Aguirre

Computer Methods in Applied Mechanics and Engineering, Volume: 276, Pages: 659 - 690

Swansea University Authors: Antonio Gil Orcid Logo, Chun Hean Lee Orcid Logo, Javier Bonet Orcid Logo

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DOI (Published version): 10.1016/j.cma.2014.04.006

Abstract

A mixed second order stabilised Petrov–Galerkin finite element framework was recently introduced by the authors (Lee et al., 2014) [46]. The new mixed formulation, written as a system of conservation laws for the linear momentum and the deformation gradient, performs extremely well in bending domina...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: 2014
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URI: https://cronfa.swan.ac.uk/Record/cronfa18295
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spelling 2020-12-18T09:11:41.8204877 v2 18295 2014-08-29 A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics 1f5666865d1c6de9469f8b7d0d6d30e2 0000-0001-7753-1414 Antonio Gil Antonio Gil true false e3024bdeee2dee48376c2a76b7147f2f 0000-0003-1102-3729 Chun Hean Lee Chun Hean Lee true false b7398206d59a9dd2f8d07a552cfd351a 0000-0002-0430-5181 Javier Bonet Javier Bonet true false 2014-08-29 CIVL A mixed second order stabilised Petrov–Galerkin finite element framework was recently introduced by the authors (Lee et al., 2014) [46]. The new mixed formulation, written as a system of conservation laws for the linear momentum and the deformation gradient, performs extremely well in bending dominated scenarios (even when linear tetrahedral elements are used) yielding equal order of convergence for displacements and stresses. In this paper, this formulation is further enhanced for nearly and truly incompressible deformations with three key novelties. First, a new conservation law for the Jacobian of the deformation is added into the system providing extra flexibility to the scheme. Second, a variationally consistent Petrov–Galerkin stabilisation methodology is derived. Third, an adapted fractional step method is presented for both incompressible and nearly incompressible materials in the context of nonlinear elastodynamics. For completeness and ease of understanding, these three improvements are presented both in small and large strain regimes, studying the eigenstructure of the resulting systems. A series of numerical examples are presented in order to demonstrate the robustness of the enhanced methodology with respect to the work previously published by the authors. Journal Article Computer Methods in Applied Mechanics and Engineering 276 659 690 0045-7825 1 7 2014 2014-07-01 10.1016/j.cma.2014.04.006 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2020-12-18T09:11:41.8204877 2014-08-29T18:39:03.2250657 Faculty of Science and Engineering School of Engineering and Applied Sciences - Uncategorised Antonio Gil 0000-0001-7753-1414 1 Chun Hean Lee 0000-0003-1102-3729 2 Javier Bonet 0000-0002-0430-5181 3 Miquel Aguirre 4
title A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
spellingShingle A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
Antonio Gil
Chun Hean Lee
Javier Bonet
title_short A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
title_full A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
title_fullStr A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
title_full_unstemmed A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
title_sort A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
e3024bdeee2dee48376c2a76b7147f2f
b7398206d59a9dd2f8d07a552cfd351a
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Antonio Gil
e3024bdeee2dee48376c2a76b7147f2f_***_Chun Hean Lee
b7398206d59a9dd2f8d07a552cfd351a_***_Javier Bonet
author Antonio Gil
Chun Hean Lee
Javier Bonet
author2 Antonio Gil
Chun Hean Lee
Javier Bonet
Miquel Aguirre
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 276
container_start_page 659
publishDate 2014
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2014.04.006
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 Engineering and Applied Sciences - Uncategorised{{{_:::_}}}Faculty of Science and Engineering{{{_:::_}}}School of Engineering and Applied Sciences - Uncategorised
document_store_str 0
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description A mixed second order stabilised Petrov–Galerkin finite element framework was recently introduced by the authors (Lee et al., 2014) [46]. The new mixed formulation, written as a system of conservation laws for the linear momentum and the deformation gradient, performs extremely well in bending dominated scenarios (even when linear tetrahedral elements are used) yielding equal order of convergence for displacements and stresses. In this paper, this formulation is further enhanced for nearly and truly incompressible deformations with three key novelties. First, a new conservation law for the Jacobian of the deformation is added into the system providing extra flexibility to the scheme. Second, a variationally consistent Petrov–Galerkin stabilisation methodology is derived. Third, an adapted fractional step method is presented for both incompressible and nearly incompressible materials in the context of nonlinear elastodynamics. For completeness and ease of understanding, these three improvements are presented both in small and large strain regimes, studying the eigenstructure of the resulting systems. A series of numerical examples are presented in order to demonstrate the robustness of the enhanced methodology with respect to the work previously published by the authors.
published_date 2014-07-01T03:21:25Z
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