An exact Riemann solver for one‐dimensional multimaterial elastic‐plastic flows with Mie‐Grüneisen equation of state without vacuum

Abstract

AbstractIn this article, we present exact Riemann solvers for the Riemann problem and the half Riemann problem, respectively, for one‐dimensional multimaterial elastic‐plastic flows with the Mie‐Grüneisen equation of state (EOS), hypoelastic constitutive model, and the von Mises' yielding condition. We first analyze the Jacobian matrices in the elastic and plastic states, and then build the relations of different variables across different type of waves. Based on these formulations, an exact Riemann solver is constructed with totally 36 possible cases of wave structures. A large number of tests prove the rightness of the new exact Riemann solver. Moreover, an exact Riemann solver is also deduced for the half Riemann problem and its validity is tested by two examples.