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1D Exact Elastic-Perfectly Plastic Solid Riemann Solver and Its Multi-Material Application

Part of: Plastic materials, materials of stress-rate and internal-variable type Special kinds of problems Equations of mathematical physics and other areas of application Coupling of solid mechanics with other effects Hyperbolic equations and systems

Published online by Cambridge University Press:  17 January 2017

Si Gao  and
Tiegang Liu
Si Gao*
Affiliation:
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
Tiegang Liu*
Affiliation:
LMIB and School of Mathematics and Systems Science, Beihang University, Beijing 100191, China
*
*Corresponding author. Email:gaos@buaa.edu.cn (S. Gao), liutg@buaa.edu.cn (T. G. Liu)
*Corresponding author. Email:gaos@buaa.edu.cn (S. Gao), liutg@buaa.edu.cn (T. G. Liu)
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Abstract

The equation of state (EOS) plays a crucial role in hyperbolic conservation laws for the compressible fluid. Whereas, the solid constitutive model with elastic-plastic phase transition makes the analysis of the solid Riemann problem more difficult. In this paper, one-dimensional elastic-perfectly plastic solid Riemann problem is investigated and its exact Riemann solver is proposed. Different from previous works treating the elastic and plastic phases integrally, we resolve the elastic wave and plastic wave separately to understand the complicate nonlinear waves within the solid and then assemble them together to construct the exact Riemann solver for the elastic-perfectly plastic solid. After that, the exact solid Riemann solver is associated with the fluid Riemann solver to decouple the fluid-solid multi-material interaction. Numerical tests, including gas-solid, water-solid high-speed impact problems are simulated by utilizing the modified ghost fluid method (MGFM).

Keywords

Riemann problemelastic-plastic solidghost fluid methodmulti-material flows

MSC classification

Secondary: 35L50: Initial-boundary value problems for first-order hyperbolic systems 35Q74: PDEs in connection with mechanics of deformable solids 74C05: Small-strain, rate-independent theories (including rigid-plastic and elasto-plastic materials) 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 74M20: Impact
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 9 , Issue 3 , June 2017 , pp. 621 - 650
Copyright
Copyright © Global-Science Press 2017 

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