A Godunov-type discrete element model for elastic-viscoplastic continuum impact problems

The discrete element model (DEM) has attractive advantages in expressing multiple cracks propagation problem in continuum, but the description of material plastic characteristics by current DEM is restricted by the connection model, which is the core procedure in DEM modeling process. A Godunov-type continuum-based DEM model is proposed to solve the dynamic response of materials under high-speed impact, in which there is a state transition of material model from continuous to discontinuous. In this article, under the framework of DEM, the contact discontinuity between adjacent elements is analyzed with the Godunov method, and a connection model derived from the physical process is established. Firstly, the numerical solution of the Riemann problem, which is equivalent to the plane wave collision operator, is solved by an iterative method, and an explicit time-marching integral format for the dynamic impact problem in elastic-viscoplastic materials is derived. Then, the numerical model is validated by comparing the calculation results with theoretical results, using a wave propagation example in plate. In addition, the capacity of simulating material property discontinuity and multiple cracks are validated by cases of stress wave transmission and reflection at the materials interface and the cracks capture in Kalthoff dynamic shear test, respectively.