Predicting the Coefficient of Restitution of Impacting Elastic-Perfectly Plastic Spheres

The current work presents a new methodology for modeling the impact between elasto-plastic spheres. Recent finite element results modeling the static deformation of an elasto-plastic sphere are used in conjunction with equations for the variation of kinetic energy to obtain predictions for the coefficient of restitution. A model is also needed to predict the residual deformation of the sphere during rebound, or unloading, of which, several are available and compared in this work. The model predicts that a significant amount of energy will be dissipated in the form of plastic deformation such that as the speed at initial impact increases, the coefficient of restitution decreases. This is due to the maximum contact force also increasing as the initial speed at impact increases. This work also derives the initial critical speed which causes plastic deformation in the sphere and decreases the coefficient of restitution below a value of one for the completely elastic case.