Cell-centered Lagrangian Lax–Wendroff HLL hybrid method for elasto-plastic flows

•A new numerical method for elasto-plastic dynamics described by Wilkins model is proposed.•Conservation laws are approximated by a cell-centered Lax–Wendroff HLL hybrid scheme.•The evolution of constitutive law is treated by method introduced by Maire et al.•Several numerical tests show reasonable performance of the method. The Wilkins hypoelastic model of the solid dynamics is numerically treated by the cell-centered Lagrangian Lax–Wendroff HLL hybrid scheme proposed recently for the Lagrangian hydrodynamics. The scheme is applied to the mass, momentum and energy conservation laws, while the elastic part of the incremental constitutive law is treated by the numerical method introduced by Maire et. al. [P.H. Maire et. al., J, Comput. Phys. 235:626,(2013)] and the plastic part by the Wilkins radial return. The performance of the numerical scheme is demonstrated on several test cases.