The Influence of Compressibility on the Restitution Coefficient for Viscoelastic Spheres in Low-Velocity Normal Impacts

TL;DR

This study investigates how material compressibility affects the restitution coefficient during low-velocity impacts of viscoelastic spheres, revealing significant underestimations when assuming incompressibility, especially in high energy dissipation scenarios.

Contribution

It introduces a numerical approach to quantify the impact of compressibility on restitution coefficients in viscoelastic impacts, highlighting potential errors in common assumptions.

Findings

Compressibility significantly influences restitution coefficients.

Assuming incompressibility can lead to over 100% error.

High energy dissipation amplifies the effect of compressibility.

Abstract

The influence of compressibility on the coefficient of restitution in the normal impact of a rigid sphere onto a linear-viscoelastic compressible standard solid under quasi-static conditions is studied using a numerical solution procedure for the contact-impact problem based on the Method of Dimensionality Reduction. We find that the influence of compressible material behavior is most significant in parameter combinations with high energy dissipation in the bulk material during the impact. Thereby the restitution coefficient is usually underestimated, if the material is assumed to be incompressible. This misestimating can be very significant (relative errors of 100% and more are possible), even, if the actual Poisson ratio is very close to 0.5.