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An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications / Jibran Haider; Chun Hean Lee; Antonio J. Gil; Antonio Huerta; Javier Bonet

Computer Methods in Applied Mechanics and Engineering, Volume: 340, Pages: 684 - 727

Swansea University Author: Gil, Antonio

  • Accepted Manuscript under embargo until: 25th June 2019

Abstract

The paper presents a new computational framework for the numerical simulation of fast large strain solid dynamics, with particular emphasis on the treatment of near incompressibility. A complete set of first order hyperbolic conservation equations expressed in terms of the linear momentum and the mi...

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Published in: Computer Methods in Applied Mechanics and Engineering
ISSN: 00457825
Published: 2018
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa40728
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Abstract: The paper presents a new computational framework for the numerical simulation of fast large strain solid dynamics, with particular emphasis on the treatment of near incompressibility. A complete set of first order hyperbolic conservation equations expressed in terms of the linear momentum and the minors of the deformation (namely the deformation gradient, its co-factor and its Jacobian), in conjunction with a polyconvex nearly incompressible constitutive law, is presented. Taking advantage of this elegant formalism, alternative implementations in terms of entropy-conjugate variables are also possible, through suitable symmetrisation of the original system of conservation variables. From the spatial discretisation standpoint, modern Computational Fluid Dynamics code “OpenFOAM” [http://www.openfoam.com/] is here adapted to the field of solid mechanics, with the aim to bridge the gap between computational fluid and solid dynamics. A cell centred finite volume algorithm is employed and suitably adapted. Naturally, discontinuity of the conservation variables across control volume interfaces leads to a Riemann problem, whose resolution requires special attention when attempting to model materials with predominant nearly incompressible behaviour (κ∕μ≥500). For this reason, an acoustic Riemann solver combined with a preconditioning procedure is introduced. In addition, a global a posteriori angular momentum projection procedure proposed in Haider et al. (2017) is also presented and adapted to a Total Lagrangian version of the nodal scheme of Kluth and Després (2010) used in this paper for comparison purposes. Finally, a series of challenging numerical examples is examined in order to assess the robustness and applicability of the proposed methodology with an eye on large scale simulation in future works.
Keywords: First order conservation laws; Large strain solid dynamics; Finite volume method; Riemann solver; OpenFOAM
College: College of Engineering
Start Page: 684
End Page: 727