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.

中文翻译：

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弹-粘塑性连续体冲击问题的Godunov型离散元模型

离散元模型（DEM）在表达连续体中的多裂纹扩展问题方面具有诱人的优势，但目前DEM对材料塑性特性的描述受到连接模型的限制，而连接模型是DEM建模过程中的核心过程。提出了一种基于Godunov型连续介质的DEM模型来解决材料在高速冲击下的动态响应，其中材料模型从连续到不连续的状态转换。本文在DEM框架下，利用Godunov方法分析了相邻单元之间的接触不连续性，建立了由物理过程导出的连接模型。首先，等价于平面波碰撞算子的黎曼问题的数值解通过迭代法求解，并且推导出了弹性-粘塑性材料中动态冲击问题的显式时间推进积分格式。然后，通过将计算结果与理论结果进行比较，以平板中的波传播为例，验证了数值模型。此外，分别通过材料界面处应力波传输和反射以及Kalthoff动态剪切试验中的裂纹捕获情况验证了模拟材料特性不连续性和多裂纹的能力。