Inelastic impact of a sphere on a massive plane: nonmonotonic velocity-dependence of the restitution coefficient

TL;DR

This study investigates how the coefficient of restitution varies nonmonotonically with impact velocity in sphere-plane collisions, revealing complex dynamics influenced by vibrational modes and particle size.

Contribution

It demonstrates the nonmonotonic velocity dependence of restitution coefficient and highlights the influence of vibrational dynamics and particle size, which are not accounted for in existing models.

Findings

Coefficient of restitution varies nonmonotonically with impact velocity.

Impact contact time is comparable to vibrational mode timescales of the plate.

Restitution coefficient decreases with increasing particle size.

Abstract

We have studied the coefficient of restitution, $\eta$, in normal collisions of a non-rotating sphere on a massive plate for a range of material parameters, impact velocity and sphere size. The measured coefficient of restitution does not monotonically vary with velocity. This effect is due to dynamics that occur during the finite duration of impact: the contact time varies as a function of velocity is comparable to the time-scales of the vibrational modes of the plate. The measured effect is robust and is expected to be ubiquitous in fluidized granular media. We also find that $\eta$ is a decreasing function of particle size, a dependence that is not captured by existing models of impact.