Diffuse interface model for compressible fluid – Compressible elastic–plastic solid interaction

Abstract

An Eulerian hyperbolic diffuse interface model for elastic–plastic solid–fluid interaction is constructed. The system of governing equations couples Euler equations of compressible fluids and a visco-plastic model of Maxwell type materials (the deviatoric part of the stress tensor decreases during plastic deformations) in the same manner as models of multicomponent fluids. In particular, the model is able to create interfaces which were not present initially.The model is thermodynamically compatible: it verifies the entropy inequality. However, a numerical treatment of the model is particularly challenging. Indeed, the model is non-conservative, so a special numerical splitting is proposed to overcome this difficulty. The numerical algorithm contains two relaxation procedures. One of them is physical and is related to the plastic relaxation mechanism (relaxation toward the yield surface). The second one is numerical. It consists in replacing the algebraic equation expressing a mechanical equilibrium between components by a partial differential equation with a short relaxation time. The numerical method was tested in 1D case (Wilkins’ flying plate problem), 2D plane case (impact of a projectile on a plate) and axisymmetrical case (Taylor test problem, impact with penetration effects, etc.). Numerical examples show the ability of the model to deal with real physical phenomena.