1D Exact Elastic-Perfectly Plastic Solid Riemann Solver and Its Multi-Material Application (Advances in Applied Mathematics and Mechanics, 2018)
The equation of state (EOS) plays a crucial role in hyperbolic conservationlaws for the compressible fluid. Whereas, the solid constitutive model with elastic-plasticphase transition makes the analysis of the solid Riemann problem more difficult. In this paper, one-dimensional elastic-perfectly plastic solid Riemann problem isinvestigated and its exact Riemann solver is proposed. Different from previous workstreating the elastic and plastic phases integrally, we resolve the elastic wave and plasticwave separately to understand the complicate nonlinear waves within the solidand then assemble them together to construct the exact Riemann solver for the elastic-perfectlyplastic solid. After that, the exact solid Riemann solver is associated with thefluid Riemann solver to decouple the fluid-solid multi-material interaction. Numericaltests, including gas-solid, water-solid high-speed impact problems are simulatedby utilizing the modified ghost fluid method (MGFM).