Approximate analytical coefficient of restitution formulation for single bead impact with external load, using nonlinear visco-elastic models

This work is largely concerned with the calculation of an approximate coefficient of restitution (CoR) associated with nonlinear spring/dashpot models, when a constant external load acts upon the colliding body. Some of the main applications concern well known visco-elastic models such as Kuwabara-Kono, Simon-Hunt-Crosseley, Tsuji-Tanaka-Ishida, etc, however the proposed approach to a very wide class of nonlinear visco-elastic contact models. It is shown that suitable expansions allow to derive a computable expression which provides accurate predictions in a valuable range of external loads and viscosity coefficients.