The complete exact Riemann solution for one-dimensional elastic–perfectly plastic Riemann problem

Abstract

In this paper, the wave structures of one-dimensional elastic–perfectly plastic solid Riemann problem are analyzed in elastic, plastic and elastic–plastic phases respectively. The research effort focuses on basic properties of the shock transition for the Wilkins model with Mie–Grüneisen equation of state (EOS). As a result of shock theory, the characters of Hugoniot curve and function of pure elastic and plastic are discussed. Especially, the wave structure in the presence of very strong shock transition from the elastic state to plastic state is researched, and the corresponding Hugoniot curve is given. Based on these analyses, the complete exact Riemann solution for the model is obtained, in which forty-nine possible solution types in total are found and enumerated for the first time. In addition, we exhibit the criteria for each wave-type and construct the complete exact Riemann solver. Several numerical tests are presented to prove the correctness of this exact Riemann solver.