An HLLC-type approximate Riemann solver for two-dimensional elastic-perfectly plastic model

•Characteristic analyses are performed for elastic and plastic phases respectively.•The order of stress waves of an augmented one–dimensional problem is researched.•A new multi-wave HLLC-type approximate Riemann solver is proposed.•The solver includes almost all elastic, plastic and shear waves simultaneously.•A cell-centered Lagrangian method with the HLLC-type Riemann solver is developed.