Coefficient of restitution for elastic disks

TL;DR

This paper derives the velocity-dependent coefficient of restitution for elastic disks from a microscopic model, showing agreement with Hertz in quasistatic limit and predicting inelastic collisions at finite velocities, influenced by material properties.

Contribution

It introduces a microscopic model for elastic disks that predicts velocity-dependent restitution and incorporates material elastic constants, extending previous theories.

Findings

$psilon$ depends on relative velocity of disks

Elastic vibrations absorb kinetic energy more in materials with low shear modulus

Theory agrees with Hertz in quasistatic limit

Abstract

We calculate the coefficient of restitution, $\epsilon$, starting from a microscopic model of elastic disks. The theory is shown to agree with the approach of Hertz in the quasistatic limit, but predicts inelastic collisions for finite relative velocities of two approaching disks. The velocity dependence of $\epsilon$ is calculated numerically for a wide range of velocities. The coefficient of restitution furthermore depends on the elastic constants of the material via Poisson's number. The elastic vibrations absorb kinetic energy more effectively for materials with low values of the shear modulus.