An upwind cell centred Total Lagrangian finite volume algorithm for nearly incompressible explicit fast solid dynamic applications
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...
| Autores: | , , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/125487 |
| Acceso en línea: | https://hdl.handle.net/2117/125487 https://dx.doi.org/10.1016/j.cma.2018.06.010 |
| Access Level: | acceso abierto |
| Palabra clave: | Difference equations, Partial--Numerical solutions Elasticity First order conservation laws Large strain solid dynamics Finite volume method Riemann solver OpenFOAM Equacions diferencials parcials--solucions numèriques Elasticitat Classificació AMS::65 Numerical analysis::65M Partial differential equations, initial value and time-dependent initial-boundary value problems Classificació AMS::74 Mechanics of deformable solids::74S Numerical methods Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica aplicada a les ciències |
| Sumario: | 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 (). 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. |
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