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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 J. Gil; Chun Hean Lee; Javier Bonet; Rogelio Ortigosa

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

Swansea University Author: Gil, Antonio

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: 2016
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URI: https://cronfa.swan.ac.uk/Record/cronfa26096
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spelling 2018-04-30T23:54:12Z 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 Antonio Gil Antonio Gil true 0000-0001-7753-1414 false 1f5666865d1c6de9469f8b7d0d6d30e2 d66249f916a874bda4f708760a8d2027 Gy3Cg4qrL2LY4pTET3406oJSbZF11mHm1K8NtCGVMYw= 2016-02-05 EEN 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 0045-7825 1 3 2016 2016-03-01 10.1016/j.cma.2015.11.010 College of Engineering Engineering CENG EEN None 2018-04-30T23:54:12Z 2016-02-05T16:55:12Z College of Engineering Engineering Antonio J. Gil 1 Chun Hean Lee 2 Javier Bonet 3 Rogelio Ortigosa 4 0026096-17022016155406.pdf GilFirstOrderHyperbolicFramework2015Postprint.pdf 2016-02-17T15:54:06Z Output 8139147 application/pdf AM true Updated Copyright 17/02/2016 2016-11-22T00:00:00 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
Gil, Antonio
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
author_id_fullname_str_mv 1f5666865d1c6de9469f8b7d0d6d30e2_***_Gil, Antonio
author Gil, Antonio
author2 Antonio J. Gil
Chun Hean Lee
Javier Bonet
Rogelio Ortigosa
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 300
container_start_page 146
publishDate 2016
institution Swansea University
issn 0045-7825
doi_str_mv 10.1016/j.cma.2015.11.010
college_str College of Engineering
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hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
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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 2016-03-01T04:38:06Z
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