Modeling Inelastic Collisions With the Hunt–Crossley Model Using the Energetic Coefficient of Restitution

Abstract

Modeling collision and contact accurately is essential to simulating many multibody systems. The three parameter Hunt–Crossley model is a continuous collision model for representing the contact dynamics of viscoelastic systems. By augmenting Hertz's elastic theory with a nonlinear damper, Hunt and Crossley captured part of the viscoelastic and velocity dependent behavior found in many systems. In the Hunt–Crossley model, the power parameter and the elastic coefficient can be related to the physical properties through Hertz's elastic theory but the damping coefficient cannot. Generally, the damping coefficient is related to an empirical measurement, the coefficient of restitution. Over the past few decades, several authors have posed relationships between the coefficient of restitution and the damping constant but key challenges remain. In the first portion of the paper, we derive an approximate expression for Stronge's (energetic) coefficient of restitution that has better accuracy for high velocities and low coefficient of restitution values than the published solutions based on Taylor series approximations. We present one method for selecting the model parameters from five empirical measurements using a genetic optimization routine. In the second portion of the paper, we investigate the application of the Hunt–Crossley model to an inhomogeneous system of a rubber covered aluminum sphere on a plate. Although this system does not fit the inclusion criteria for the Hunt–Crossley, it is representative of many systems of interest where authors have chosen the Hunt–Crossley model to represent the contact dynamics. The results show that a fitted model well predicts collision behavior at low values of the coefficient of restitution.