An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications

Haider, J., Lee, C. H. , Gil, A. J., Huerta, A. and Bonet, J. (2018) An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications. Computer Methods in Applied Mechanics and Engineering, 340, pp. 684-727. (doi: 10.1016/j.cma.2018.06.010)

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.

• Item Type: Articles
• Additional Information: The first author acknowledges the financial support provided by “The Erasmus Mundus Joint Doctorate SEED” programme and the European Regional Development Fund (ERDF) funded project “ASTUTE 2020 Operation”. The second and third authors would like to acknowledge the financial support received through the Sér Cymru National Research Network for Advanced Engineering and Materials, United Kingdom .
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Lee, Dr Chun Hean
• Authors: Haider, J., Lee, C. H., Gil, A. J., Huerta, A., and Bonet, J.
• College/School: College of Science and Engineering > School of Engineering > Infrastructure and Environment
• Journal Name: Computer Methods in Applied Mechanics and Engineering
• Journal Abbr.: CMAME
• Publisher: Elsevier
• ISSN: 0045-7825
• ISSN (Online): 1879-2138
• Published Online: 25 June 2018
• Copyright Holders: Copyright © 2018 Elsevier B.V.
• First Published: First published in Computer Methods in Applied Mechanics and Engineering 340: 684-727
• Publisher Policy: Reproduced in accordance with the publisher copyright policy