An HLLC-type approximate Riemann solver for two-dimensional elastic-perfectly plastic model
Abstract null null In this work, an elastic-perfectly plastic model in two-dimensional planar geometry is studied and a new HLLC-type approximate Riemann solver (HLLCN) is put forward. The main feature of the new approximate Riemann solver is that it almost includes all stress waves, such as elastic, plastic, longitudinal and shear waves simultaneously in the presence of elastic-plastic phase transition. The analyses of the Jacobian matrix of governing equations are carried out for elasticity and plasticity separately, and the complicate order in the light of magnitude of characteristic speeds is simplified when constructing the approximate Riemann solver. The radial return mapping algorithm originally proposed by Wilkins is not only applied for the plastic correction in the discretization of the constitutive law, but also used to determine the elastic limit state in the approximate Riemann solver. A cell-centered Lagrangian method equipped with this new HLLC-type approximate Riemann solver is developed. Typical and new devised test cases are provided to demonstrate the performance of proposed method.