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A Cartesian Scheme for Compressible Multimaterial Hyperelastic Models with Plasticity

  • Alexia de Brauer (a1), Angelo Iollo (a1) and Thomas Milcent (a2)

We describe a numerical model to simulate the non-linear elasto-plastic dynamics of compressible materials. The model is fully Eulerian and it is discretized on a fixed Cartesian mesh. The hyperelastic constitutive law considered is neohookean and the plasticity model is based on a multiplicative decomposition of the inverse deformation tensor. The model is thermodynamically consistent and it is shown to be stable in the sense that the norm of the deviatoric stress tensor beyond yield is non increasing. The multimaterial integration scheme is based on a simple numerical flux function that keeps the interfaces sharp. Numerical illustrations in one to three space dimensions of high-speed multimaterial impacts in air are presented.

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*Corresponding author. Email addresses: de Brauer), Iollo), Milcent)
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[1] Barton P.T., Deiterding R., Meiron D., and Pullin D.. Eulerian adaptative finite difference method for high-velocity impact and penetration problems. Journal of Computational Physics, 240:7699, 2013.
[2] Barton P.T., Drikakis D., Romenski E., and Titarev V.A.. Exact and approximate solutions of Riemann problems in non-linear elasticity. Journal of Computational Physics, 228(18):70467068, 2009.
[3] Cottet G.H., Maitre E., and Milcent T.. Eulerian formulation and level set models for incompressible fluid-structure interaction. ESAIM: Mathematical Modelling and Numerical Analysis, 42:471492, 2008.
[4] Davis S.. Simplified second-order Godunov-type methods. SIAM Journal on Scientific and Statistical Computing, 9(3):445473, 1988.
[5] de Brauer A., Iollo A., and Milcent T.. A Cartesian scheme for compressible multimaterial models in 3d. Journal of Computational Physics, 313:121143, 2016.
[6] Favrie N. and Gavrilyuk S. L.. Diffuse interface model for compressible fluid – Compressible elastic-plastic solid interaction. Journal of Computational Physics, 231(7):26952723, 2012.
[7] Favrie N. and Gavrilyuk S.L.. Dynamics of shock waves in elastic-plastic solids. ESAIM: Proceedings, 33:5067, 2011.
[8] Favrie N., Gavrilyuk S.L., and Saurel R.. Solid-fluid diffuse interface model in cases of extreme deformations. Journal of Computational Physics, 228(16):60376077, 2009.
[9] Gavrilyuk S.L., Favrie N., and Saurel R.. Modelling wave dynamics of compressible elastic materials. Journal of Computational Physics, 227(5):29412969, 2008.
[10] Godunov S.K.. Elements of continuum mechanics. Nauka Moscow, 1978.
[11] Gorsse Y., Iollo A., Milcent T., and Telib H.. A simple cartesian scheme for compressible multimaterials. Journal of Computational Physics, 272:772798, 2014.
[12] Hill D.J., Pullin D., Ortiz M., and Meiron D.. An Eulerian hybridWENO centered-difference solver for elasticplastic solids. Journal of Computational Physics, 229(24):90539072, 2010.
[13] Iollo A., Milcent T., and Telib H.. A sharp contact discontinuity scheme for multimaterial models. In Finite Volumes for Complex Applications VI, Problems & Perspectives, volume 4 of Springer Proceedings in Mathematics, pages 581588. Springer Berlin Heidelberg, 2011.
[14] Jiang G.S. and Shu C.W.. Efficient implementation of Weighted ENO schemes. Journal of Computational Physics, 126(1):202228, 1996.
[15] Kluth G. and Despres B.. Discretization of hyperelasticity on unstructured mesh with a cell-centered Lagrangian scheme. Journal of Computational Physics, 229(24):90929118, 2010.
[16] Lee E.H. and Liu D.T.. Finite-strain elastic-plastic theory with application to plane-wave analysis. Journal of Applied Physics, 38(1):1927, 1967.
[17] Maire P.-H., Abgrall R., Breil J., Loubère R., and Rebourcet B.. A nominally second-order cell-centered Lagrangian scheme for simulating elastic-plastic flows on two-dimensional unstructured grids. Journal of Computational Physics, 235(C):626665, 2013.
[18] Miller G.H. and Colella P.. A high-order eulerian godunov method for elasticplastic flow in solids. Journal of Computational Physics, 167(1):131176, 2001.
[19] Miller G.H. and Colella P.. A conservative three-dimensional eulerian method for coupled solid-fluid shock capturing. Journal of Computational Physics, 183(1):2682, 2002.
[20] Naghdi P.M.. A critical review of the state of finite plasticity. Zeitschrift für angewandte Mathematik und Physik ZAMP, 41(3):315394, 1990.
[21] Ndanou S., Favrie N., and Gavrilyuk S.. Multi-solid and multi-fluid diffuse interface model: Applications to dynamic fracture and fragmentation. Journal of Computational Physics, 295:523555, 2015.
[22] López Ortega A, Lombardini M, Pullin D I, and Meiron D I. Numerical simulation of elasticplastic solid mechanics using an Eulerian stretch tensor approach and HLLD Riemann solver. Journal of Computational Physics, 257(PA):414441, 2014.
[23] Plohr B.J. and Sharp D.H.. A conservative eulerian formulation of the equations for elastic flow. Advances in Applied Mathematics, 9:481499, 1988.
[24] Plohr B.J. and Sharp D.H.. A conservative formulation for plasticity. Advances in Applied Mathematics, 13:462493, 1992.
[25] Sijoy C.D. and Chaturvedi S.. An Eulerian multi-material scheme for elasticplastic impact and penetration problems involving large material deformations. European Journal of Mechanics - B/Fluids, 53:85100, 2015.
[26] Toro E.F., Spruce M., and Speares W.. Restoration of the contact surface in the HLL-Riemann solver. Shock Waves, 4:2534, 1994.
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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
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