Hydrodynamic model of a collision of a spherical plastic ice particle with a perfectly rigid substrate

Abstract

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.