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A first order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme

A first order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme

Haider, Jibran, Lee, Chun Hean, Gil, Antonio J. and Bonet, Javier ORCID: 0000-0002-0430-5181 (2016) A first order hyperbolic framework for large strain computational solid dynamics: An upwind cell centred Total Lagrangian scheme. International Journal for Numerical Methods in Engineering, 109 (3). pp. 407-456. ISSN 0029-5981 (Print), 1097-0207 (Online) (doi:https://doi.org/10.1002/nme.5293)

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Abstract

This paper builds on recent work developed by the authors for the numerical analysis of large strain solid dynamics, by introducing an upwind cell centred hexahedral Finite Volume framework implemented within the open source code OpenFOAM [http://www.openfoam.com/http://www.openfoam.com/]. In Lee, Gil and Bonet [1], a first order hyperbolic system of conservation laws was introduced in terms of the linear momentum and the deformation gradient tensor of the system, leading to excellent behaviour in two dimensional bending dominated nearly incompressible scenarios. The main aim of this paper is the extension of this algorithm into three dimensions, its tailor-made implementation into OpenFOAM and the enhancement of the formulation with three key novelties. First, the introduction of two different strategies in order to ensure the satisfaction of the underlying involutions of the system, that is, that the deformation gradient tensor must be curl-free throughout the deformation process. Second, the use of a discrete angular momentum projection algorithm and a monolithic Total Variation Diminishing Runge-Kutta time integrator combined in order to guarantee the conservation of angular momentum. Third, and for comparison purposes, an adapted Total Lagrangian version of the Hyperelastic-GLACE nodal scheme of Kluth and Despr´es [2] is presented. A series of challenging numerical examples are examined in order to assess the robustness and accuracy of the proposed algorithm, benchmarking it against an ample spectrum of alternative numerical strategies developed by the authors in recent publications.

Item Type: Article
Uncontrolled Keywords: Conservation laws; Finite Volume Method; OpenFOAM; Locking; Riemann solver; Upwind; Large strain; Solid dynamics
Subjects: Q Science > QA Mathematics > QA76 Computer software
T Technology > TA Engineering (General). Civil engineering (General)
Faculty / Department / Research Group: Vice-Chancellor's Group
Last Modified: 24 Apr 2018 14:26
Selected for GREAT 2016: None
Selected for GREAT 2017: None
Selected for GREAT 2018: GREAT a
Selected for GREAT 2019: None
URI: http://gala.gre.ac.uk/id/eprint/15531

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