Journal article 1155 views
A stabilised Petrov–Galerkin formulation for linear tetrahedral elements in compressible, nearly incompressible and truly incompressible fast dynamics
Computer Methods in Applied Mechanics and Engineering, Volume: 276, Pages: 659 - 690
Swansea University Authors:
Antonio Gil , Chun Hean Lee
, Javier Bonet
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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...
Published in: | Computer Methods in Applied Mechanics and Engineering |
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ISSN: | 0045-7825 |
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2014
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URI: | https://cronfa.swan.ac.uk/Record/cronfa18295 |
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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 |
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Computer Methods in Applied Mechanics and Engineering |
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276 |
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659 |
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2014 |
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Swansea University |
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0045-7825 |
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10.1016/j.cma.2014.04.006 |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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Faculty of Science and Engineering |
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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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1763750639571042304 |
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11.021648 |