A Robust Riemann Solver for Multiple Hydro-Elastoplastic Solid Mediums

Abstract

We propose a robust approximate solver for the hydro-elastoplastic solid material, a general constitutive law extensively applied in explosion and high speed impact dynamics, and provide a natural transformation between the fluid and solid in the case of phase transitions. The hydrostatic components of the solid is described by a family of general Mie-Gr üneisen equation of state (EOS), while the deviatoric component includes the elastic phase, linearly hardened plastic phase and fluid phase. The approximate solver provides the interface stress and normal velocity by an iterative method. The well-posedness and convergence of our solver are proved with mild assumptions on the equations of state. The proposed solver is applied in computing the numerical flux at the phase interface for our compressible multi-medium flow simulation on Eulerian girds. Several numerical examples, including Riemann problems, shock-bubble interactions, implosions and high speed impact applications, are presented to validate the approximate solver.

Simulation of Wave in Hypo-Elastic-Plastic Solids Modeled by Eulerian Conservation Laws

“…In their governing equations, derivative of the inverse deformation gradient tensor is written to become a hyperbolic differential equation with source term. A multi-medium Riemann solver was proposed by Li et al [16] to study impact dynamics between solid and fluid. Hydro-elastoplastic constitutive material model and Mie-Gruneisen equation of state are used to close the governing equations.…”