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A Cartesian Scheme for Compressible Multimaterial Hyperelastic Models with Plasticity

Part of: Hyperbolic equations and systems Plastic materials, materials of stress-rate and internal-variable type Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  31 October 2017

Alexia de Brauer ,
Angelo Iollo  and
Thomas Milcent
Alexia de Brauer*
Affiliation:
Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France. CNRS, IMB, UMR 5251, F-33400 Talence, France. INRIA, F-33400 Talence, France
Angelo Iollo*
Affiliation:
Univ. Bordeaux, IMB, UMR 5251, F-33400 Talence, France. CNRS, IMB, UMR 5251, F-33400 Talence, France. INRIA, F-33400 Talence, France
Thomas Milcent*
Affiliation:
Univ. Bordeaux, I2M, UMR 5295, F-33400 Talence, France. Arts et Métiers Paristech, F-33607 Pessac, France
*
*Corresponding author. Email addresses:alexia.de-brauer@math.u-bordeaux1.fr(A. de Brauer), angelo.iollo@math.u-bordeaux1.fr(A. Iollo), thomas.milcent@u-bordeaux.fr(T. Milcent)
*Corresponding author. Email addresses:alexia.de-brauer@math.u-bordeaux1.fr(A. de Brauer), angelo.iollo@math.u-bordeaux1.fr(A. Iollo), thomas.milcent@u-bordeaux.fr(T. Milcent)
*Corresponding author. Email addresses:alexia.de-brauer@math.u-bordeaux1.fr(A. de Brauer), angelo.iollo@math.u-bordeaux1.fr(A. Iollo), thomas.milcent@u-bordeaux.fr(T. Milcent)
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Abstract

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.

Keywords

Compressible multimaterialEulerian elasticityplasticity

MSC classification

Secondary: 35L65: Conservation laws 65M08: Finite volume methods 74C15: Large-strain, rate-independent theories (including nonlinear plasticity)
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 5 , November 2017 , pp. 1362 - 1384
Copyright
Copyright © Global-Science Press 2017 

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