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

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.