Mechanics of collisions of solids: influence of friction and adhesion. II numerical modeling

This paper is the second part of the review on the physics of two-particle collisions of solids. The first one describes theoretical and experimental works on collisions of elastic and elastic-plastic solid bodies in the case when the energy dissipation is caused by the inner or interface friction, plasticity, adhesion, or some other damping mechanisms. In this second part, we concentrate on the case of collisions of elastic particles. Results of the analytical and numerical modelling within the dimensionality reduction (MDR) method are presented. MDR allows describing a three-dimensional contact by a reduction to an equivalent problem in a one-dimensional space. We consider three cases: a collision between bodies without slipping (equivalent to an infinite coefficient of friction), with a finite coefficient of friction in the interface, and with the presence of adhesion, which is described in the JKR limit. In all the considered cases, proper dimensionless variables have been identified which fully characterize the collision process, and the functions determining the transformation of the state before the impact into the state after the impact has been determined numerically. By using these dimensionless variables, it is possible to calculate the velocity components and the angular velocity, and hence the trajectory of the ball after the collision, in case if analogous parameters are known before the collision. Theoretical results are compared with the available results, the experimental data show agree well with the experiments.