Impact of a single particle onto a rigid substrate leads to its deformation and subsequent fragmentation. In this theoretical study a simplified model for the plastic flow in a deforming particle is developed which accounts for the dependence of the yield strength on the effective local strain rate. The flow in the particle is approximated by an incompressible inviscid flow which satisfies the conditions of impenetrability of the substrate. The expression for the pressure field in the particle is obtained from the momentum balance equations. This expression includes the plastic stresses, the inertial effects associated with the typical particle velocity and the effects, associated with the particle deceleration. The theoretical predictions for the maximum force, for the force evolution and for the evolution of the particle height agree well with the experimental data found in the literature. No adjustable parameters used in the model.

单个颗粒撞击刚性基材会导致其变形和随后的碎裂。在这项理论研究中，开发了变形粒子中塑性流动的简化模型，该模型解释了屈服强度对有效局部应变率的依赖性。粒子中的流动近似于满足基材不可渗透条件的不可压缩的无粘性流动。粒子内压力场的表达式由动量平衡方程得到。该表达式包括塑性应力、与典型粒子速度相关的惯性效应以及与粒子减速相关的效应。最大力的理论预测，力演化和粒子高度演化与文献中的实验数据非常吻合。模型中没有使用可调参数。