Coefficients of restitution based on a fractal surface model

Equations of rigid-body mechanics provide a means to predict the post-collision behavior without recourse to highly complex, detailed analysis of deformations during contact. Before the prediction can be completed, the coefficient of restitution, which relates the rebound velocity to the incident velocity, must be estimated properly. The coefficient of restitution depends on the surface topography in addition to the material properties and incident velocity. Recent investigations showed that surface topography can be characterized properly by fractal models. This paper proposes a normal contact model for a fractal surface in contact with a rigid smooth half-space. The fractal surface is constructed based on the Cantor set and composed of elastic-perfectly plastic material. Asymptotic continuous expressions for the load-displacement relations during loading and unloading are derived. Based on these results, we study the effects of surface roughness, material properties and incident velocity on the coefficient of restitution.