Coefficient of tangential restitution for the linear dashpot model

TL;DR

This paper analyzes the tangential restitution coefficient in the linear dashpot model, revealing velocity-dependent behavior that enhances the accuracy of granular system simulations involving frictional particles.

Contribution

It provides analytical and numerical determination of the tangential restitution coefficient for common tangential force models, highlighting its velocity dependence.

Findings

The normal restitution coefficient remains constant in the linear dashpot model.

The tangential restitution coefficient varies with impact velocity.

Results can improve event-driven simulations of frictional granular particles.

Abstract

The linear dashpot model for the inelastic normal force between colliding spheres leads to a constant coefficient of normal restitution, $\epsilon_n=$const., which makes this model very popular for the investigation of dilute and moderately dense granular systems. For two frequently used models for the tangential interaction force we determine the coefficient of tangential restitution $\epsilon_t$, both analytically and by numerical integration of Newton's equation. Although $\epsilon_n=$const. for the linear-dashpot model, we obtain pronounced and characteristic dependencies of the tangential coefficient on the impact velocity $\epsilon_t=\epsilon_t(\vec{g})$. The results may be used for event-driven simulations of granular systems of frictional particles.