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A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity / Javier Bonet; Antonio J. Gil; Chun Hean Lee; Miquel Aguirre; Rogelio Ortigosa

Computer Methods in Applied Mechanics and Engineering, Volume: 283, Pages: 689 - 732

Swansea University Author: Bonet, Javier

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DOI (Published version): 10.1016/j.cma.2014.09.024

Abstract

This paper introduces a new computational framework for the analysis of large strain fast solid dynamics. The paper builds upon previous work published by the authors (Gil et al., 2014) [48], where a first order system of hyperbolic equations is introduced for the simulation of isothermal elastic ma...

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Published in: Computer Methods in Applied Mechanics and Engineering
Published: 2015
URI: https://cronfa.swan.ac.uk/Record/cronfa19836
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spelling 2016-10-10T10:54:43Z v2 19836 2015-01-03 A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity Javier Bonet Javier Bonet false 0000-0002-0430-518 false b7398206d59a9dd2f8d07a552cfd351a 6adf1fe75ad5f58f0e1c7e5448ea56b0 Mj+79iOJYGR2FSbJqEoS84JSbZF11mHm1K8NtCGVMYw= 2015-01-03 CENG This paper introduces a new computational framework for the analysis of large strain fast solid dynamics. The paper builds upon previous work published by the authors (Gil et al., 2014) [48], where a first order system of hyperbolic equations is introduced for the simulation of isothermal elastic materials in terms of the linear momentum, the deformation gradient and its Jacobian as unknown variables. In this work, the formulation is further enhanced with four key novelties. First, the use of a new geometric conservation law for the co-factor of the deformation leads to an enhanced mixed formulation, advantageous in those scenarios where the co-factor plays a dominant role. Second, the use of polyconvex strain energy functionals enables the definition of generalised convex entropy functions and associated entropy fluxes for solid dynamics problems. Moreover, the introduction of suitable conjugate entropy variables enables the derivation of a symmetric system of hyperbolic equations, dual of that expressed in terms of conservation variables. Third, the new use of a tensor cross product [61] greatly facilitates the algebraic manipulations of expressions involving the co-factor of the deformation. Fourth, 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. As an example, a polyconvex Mooney–Rivlin material is used and, for completeness, the eigen-structure of the resulting system of equations is studied to guarantee the existence of real wave speeds. Finally, a series of numerical examples is presented in order to assess the robustness and accuracy of the new mixed methodology, benchmarking it against an ample spectrum of alternative numerical strategies, including implicit multi-field Fraeijs de Veubeke–Hu–Washizu variational type approaches and explicit cell and vertex centred Finite Volume schemes. Journal article Computer Methods in Applied Mechanics and Engineering 283 689 732 1 1 2015 2015-01-01 10.1016/j.cma.2014.09.024 College of Engineering College CENG CENG None None 2016-10-10T10:54:43Z 2015-01-03T21:13:37Z College of Engineering Engineering Javier Bonet 1 Antonio J. Gil 2 Chun Hean Lee 3 Miquel Aguirre 4 Rogelio Ortigosa 5
title A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity
spellingShingle A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity
Bonet, Javier
title_short A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity
title_full A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity
title_fullStr A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity
title_full_unstemmed A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity
title_sort A first order hyperbolic framework for large strain computational solid dynamics. Part I: Total Lagrangian isothermal elasticity
author_id_str_mv b7398206d59a9dd2f8d07a552cfd351a
author_id_fullname_str_mv b7398206d59a9dd2f8d07a552cfd351a_***_Bonet, Javier
author Bonet, Javier
author2 Javier Bonet
Antonio J. Gil
Chun Hean Lee
Miquel Aguirre
Rogelio Ortigosa
format Journal article
container_title Computer Methods in Applied Mechanics and Engineering
container_volume 283
container_start_page 689
publishDate 2015
institution Swansea University
doi_str_mv 10.1016/j.cma.2014.09.024
college_str College of Engineering
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hierarchy_top_id collegeofengineering
hierarchy_top_title College of Engineering
hierarchy_parent_id collegeofengineering
hierarchy_parent_title College of Engineering
department_str Engineering{{{_:::_}}}College of Engineering{{{_:::_}}}Engineering
document_store_str 0
active_str 0
description This paper introduces a new computational framework for the analysis of large strain fast solid dynamics. The paper builds upon previous work published by the authors (Gil et al., 2014) [48], where a first order system of hyperbolic equations is introduced for the simulation of isothermal elastic materials in terms of the linear momentum, the deformation gradient and its Jacobian as unknown variables. In this work, the formulation is further enhanced with four key novelties. First, the use of a new geometric conservation law for the co-factor of the deformation leads to an enhanced mixed formulation, advantageous in those scenarios where the co-factor plays a dominant role. Second, the use of polyconvex strain energy functionals enables the definition of generalised convex entropy functions and associated entropy fluxes for solid dynamics problems. Moreover, the introduction of suitable conjugate entropy variables enables the derivation of a symmetric system of hyperbolic equations, dual of that expressed in terms of conservation variables. Third, the new use of a tensor cross product [61] greatly facilitates the algebraic manipulations of expressions involving the co-factor of the deformation. Fourth, 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. As an example, a polyconvex Mooney–Rivlin material is used and, for completeness, the eigen-structure of the resulting system of equations is studied to guarantee the existence of real wave speeds. Finally, a series of numerical examples is presented in order to assess the robustness and accuracy of the new mixed methodology, benchmarking it against an ample spectrum of alternative numerical strategies, including implicit multi-field Fraeijs de Veubeke–Hu–Washizu variational type approaches and explicit cell and vertex centred Finite Volume schemes.
published_date 2015-01-01T05:16:06Z
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