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A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity

Antonio Gil Orcid Logo, Chun Hean Lee Orcid Logo, Javier Bonet Orcid Logo, Rogelio Ortigosa

Computer Methods in Applied Mechanics and Engineering, Volume: 300, Pages: 146 - 181

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

Abstract

In Part I of this series, Bonet et al. (2015) introduced a new computational framework for the analysis of large strain isothermal fast solid dynamics, where a mixed set of Total Lagrangian conservation laws was presented in terms of the linear momentum and an extended set of strain measures, namely...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 0045-7825
Published: Elsevier BV 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa26096
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spelling 2020-10-06T10:24:15.3207057 v2 26096 2016-02-05 A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity 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 2016-02-05 CIVL In Part I of this series, Bonet et al. (2015) introduced a new computational framework for the analysis of large strain isothermal fast solid dynamics, where a mixed set of Total Lagrangian conservation laws was presented in terms of the linear momentum and an extended set of strain measures, namely the deformation gradient, its co-factor and its Jacobian. The main aim of this paper is to expand this formulation to the case of nearly incompressible and truly incompressible materials. The paper is further enhanced with three key novelties. First, the use of polyconvex nearly incompressible strain energy functionals enables the definition of generalised convex entropy functions and associated entropy fluxes. Two variants of the same formulation can then be obtained, namely, conservation-based and entropy-based, depending on the unknowns of the system. Crucially, the study of the eigenvalue structure of the system is carried out in order to demonstrate its hyperbolicity and, thus, obtain the correct time step bounds for explicit time integrators. Second, the development of a stabilised Petrov–Galerkin framework is presented for both systems of hyperbolic equations, that is, when expressed in terms of either conservation or entropy variables. Third, an adapted fractional step method, built upon the work presented in Gil et al. (2014), is presented to extend the range of applications towards the incompressibility limit. Finally, a series of numerical examples are presented in order to assess the applicability and robustness of the proposed formulation. The overall scheme shows excellent behaviour in compressible, nearly incompressible and truly incompressible scenarios, yielding equal order of convergence for velocities and stresses. Journal Article Computer Methods in Applied Mechanics and Engineering 300 146 181 Elsevier BV 0045-7825 Entropy variables; Conservation laws; Fast dynamics; Petrov–Galerkin; Incompressibility; Fractional step 1 3 2016 2016-03-01 10.1016/j.cma.2015.11.010 COLLEGE NANME Civil Engineering COLLEGE CODE CIVL Swansea University 2020-10-06T10:24:15.3207057 2016-02-05T16:55:12.4877732 College of Engineering Engineering Antonio Gil 0000-0001-7753-1414 1 Chun Hean Lee 0000-0003-1102-3729 2 Javier Bonet 0000-0002-0430-5181 3 Rogelio Ortigosa 4 0026096-17022016155406.pdf GilFirstOrderHyperbolicFramework2015Postprint.pdf 2016-02-17T15:54:06.8600000 Output 8139147 application/pdf Accepted Manuscript true 2016-11-22T00:00:00.0000000 true
title A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity
spellingShingle A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity
Antonio Gil
Chun Hean Lee
Javier Bonet
title_short A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity
title_full A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity
title_fullStr A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity
title_full_unstemmed A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity
title_sort A first order hyperbolic framework for large strain computational solid dynamics. Part II: Total Lagrangian compressible, nearly incompressible and truly incompressible elasticity
author_id_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2
e3024bdeee2dee48376c2a76b7147f2f
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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
Rogelio Ortigosa
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container_title Computer Methods in Applied Mechanics and Engineering
container_volume 300
container_start_page 146
publishDate 2016
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doi_str_mv 10.1016/j.cma.2015.11.010
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description In Part I of this series, Bonet et al. (2015) introduced a new computational framework for the analysis of large strain isothermal fast solid dynamics, where a mixed set of Total Lagrangian conservation laws was presented in terms of the linear momentum and an extended set of strain measures, namely the deformation gradient, its co-factor and its Jacobian. The main aim of this paper is to expand this formulation to the case of nearly incompressible and truly incompressible materials. The paper is further enhanced with three key novelties. First, the use of polyconvex nearly incompressible strain energy functionals enables the definition of generalised convex entropy functions and associated entropy fluxes. Two variants of the same formulation can then be obtained, namely, conservation-based and entropy-based, depending on the unknowns of the system. Crucially, the study of the eigenvalue structure of the system is carried out in order to demonstrate its hyperbolicity and, thus, obtain the correct time step bounds for explicit time integrators. Second, the development of a stabilised Petrov–Galerkin framework is presented for both systems of hyperbolic equations, that is, when expressed in terms of either conservation or entropy variables. Third, an adapted fractional step method, built upon the work presented in Gil et al. (2014), is presented to extend the range of applications towards the incompressibility limit. Finally, a series of numerical examples are presented in order to assess the applicability and robustness of the proposed formulation. The overall scheme shows excellent behaviour in compressible, nearly incompressible and truly incompressible scenarios, yielding equal order of convergence for velocities and stresses.
published_date 2016-03-01T03:36:56Z
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