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

Author (s): Haider, J.; Lee, C.H; Gil, A.J.; Huerta, A. and Bonet, J.
Journal: Computer Methods in Applied Mechanics and Engineering

Volume: 340
Pages: 684 – 727
Date: 2018

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 for- malism, 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 [1] is also presented and adapted to a Total Lagrangian version of the nodal scheme of Kluth and Després [2] used in this paper for comparison purposes. Finally, a series of challenging nume- rical 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.

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Bibtex:

@article {Haider-HLGHB:18,
        Author = {Jibran Haider and Chun Hean Lee and Antonio J. Gil and Antonio Huerta and Javier Bonet},
        Title = {An upwind cell centred {T}otal {L}agrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications},
        Fjournal = {Computer Methods in Applied Mechanics and Engineering},
        Journal = {Comput. Methods Appl. Mech. Eng.},
        Volume = {340},
        Pages = {684-727},
        Year = {2018},
        Doi = {10.1016/j.cma.2018.06.010},
        }