Damped Normal Compliance (DNC) and the restitution coefficient

Abstract

This work introduces and studies a novel normal compliance contact condition with damping, the Damped Normal Compliance (DNC), which is more realistic than the usual normal compliance condition that is often used in modeling contact between solids. The condition is applied in a model for the contact of a rigid mass with a reactive obstacle and allows for energy dissipation during contact. We analyze the model and show that the condition is of mathematical, as well as applied, interest. Then, we establish its relationship with the so-called “coefficient of restitution,” $e$ , and show that the concept is not well defined, since $e$ depends on the system parameters, applied force, and initial data. The various theoretical results are depicted using computer simulations.