# A Robust Riemann Solver for Multiple Hydro-Elastoplastic Solid Mediums

## TL;DR

This paper introduces a robust approximate Riemann solver for hydro-elastoplastic solids, capable of handling phase transitions and multiple mediums, validated through various high-speed impact simulations.

## Contribution

It presents a novel iterative solver with proven well-posedness and convergence for complex hydro-elastoplastic models involving phase changes.

## Key findings

- Effective in computing interface stresses and velocities
- Accurately models phase transitions in multi-medium flows
- Validated through diverse numerical experiments

## 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\"uneisen 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.