Exact restitution and generalizations for the Hunt–Crossley contact model

Abstract

The coefficient of restitution is an empirical contact parameter, determined for several combinations of materials, and is widely employed to characterize energy loss during impact. To this day, no exact solution has been proposed for determining the damping term in the generally accepted Hunt–Crossley contact model as a function of the restitution coefficient. In this article, the exact solution for this problem is finally put forth. It is further noted that the viscoelastic model, proposed by Hunt and Crossley, may generate an undesirable adhesive force, between otherwise repulsive surfaces, when external forcing terms are present. To solve this problem, efficient extensions are proposed for the viscoelastic model, which are guaranteed to be non-adhesive outside the determined compression-restitution phase. Finally, a new continuous contact model is proposed, comprising an exponential viscoelastic force of the form keηδ˙δα, which follows from the previous extensions and for which the exact implementation of restitution coefficient also applies. This new model can be seen as a generalization of the Hunt–Crossley contact model.