Coefficient of Restitution for Viscoelastic Spheres: The Effect of Delayed Recovery

TL;DR

This paper investigates how delayed shape recovery in viscoelastic spheres affects the coefficient of restitution, revealing a new impact-rate dependence overlooked in previous models.

Contribution

It introduces a correction to the restitution coefficient calculation by accounting for delayed recovery, improving accuracy in modeling viscoelastic collisions.

Findings

Coefficient of restitution depends on impact rate due to delayed recovery.

Previous models underestimated restitution by neglecting contact loss timing.

New model aligns better with experimental observations.

Abstract

The coefficient of normal restitution of colliding viscoelastic spheres is computed as a function of the material properties and the impact velocity. From simple arguments it becomes clear that in a collision of purely repulsively interacting particles, the particles loose contact slightly before the distance of the centers of the spheres reaches the sum of the radii, that is, the particles recover their shape only after they lose contact with their collision partner. This effect was neglected in earlier calculations which leads erroneously to attractive forces and, thus, to an underestimation of the coefficient of restitution. As a result we find a novel dependence of the coefficient of restitution on the impact rate.