(untitled) (Advances in Applied Mathematics and Mechanics, 2022)
A cell-centered Lagrangian scheme is developed for the numerical simulation of wave propagations in one dimensional (1D) elastic-plastic flow. The classical elastic-plastic material model initially proposed by Wilkins is adopted. The linear elastic model (Hooke’s Law), perfectly plastic model and von Mises yield criterion are used to describe the constitutive relationship of elastic-plastic solid. The second-order extension of this scheme is achieved by a linear reconstruction method. Various numerical tests are simulated to check the capability of this scheme in capturing nonlinear elastic-plastic waves. Compared with the well-developed operator splitting method used in simulating elastic-plastic flow, this scheme is more accurate due to the consideration of a list of 64 different types of the nonlinear elastic-plastic waves when constructing the elastic-perfectly plastic Riemann solver. The numerical simulations of typical examples show competitive results.