Effect of plasticity on the coefficient of restitution of an elastoplastic sphere impacting an elastic plate

Abstract

A sphere impacting a plate is different from impacting a half-space bulk, because energy in the former case can be dissipated in a form of flexural wave propagating on the plate. Such energy loss by the elastic wave can be explained by the Zener model; however, this model is only valid for low-velocity impact with elastic Hertzian contact law. For high-velocity impact with contact plasticity, the Zener model is not valid any ore because energy dissipation by plasticity may take a large fraction, so that the Zener model, which ignores plasticity, will overestimate the coefficient of restitution (COR). In order to study how much the plasticity affects the sphere impacting the plate, we developed a modified Zener model by employing the contact plasticity into the controlling equation. Using the developed model, we firstly presented a thickness-dependent yielding velocity (yielding impact velocity depends on the thickness of the plate), above which the contact plasticity should be taken into account. What is more, we presented a semi-analytical solution to predict the COR over a large range of plate thickness. Meanwhile, finite element simulations were carried out to prove that the present model can give enough accuracy for the high velocity impact.