Mechanics of collisions of solids: influence of friction and adhesion. I. Review of experimental and theoretical works

Collisions of solid bodies are of significant interest for a great variety of physical and engineering applications. This review is devoted to non-elastic collisions of solid bodies when the energy dissipation is caused by the inner or interface friction, plasticity, adhesion, or other damping mechanisms. We consider only two-particle collisions. This impact problem can be reduced to the collision of a solid particle with a half-space. We discuss the collision without slip (infinite coefficient of friction) and in the presence of a finite coefficient of friction, as well as in the presence of adhesion between contacting bodies. A review is given of the previous theoretical and experimental work on both elastic and non-elastic impacts. However, the focus of the present work is on collisions of elastic particles. We consider the general oblique impact with non-zero normal and tangential velocity components of impacting particles. Analytical expressions for the restitution coefficient obtained by many authors are presented. Generally, the restitution coefficient depends on adhesive and plastic properties of contacting bodies. High velocity impact with destruction of particles does not belong to the scope of the paper. This paper is the first part of a two-parts-review. In the second part the results of analytical and numerical simulations will be presented, which have been obtained by the authors using the method of dimensionality reduction, allowing for reduction of three-dimensional contact problems to a much simpler equivalent problem in a one-dimensional space.