Two novel semi-analytical coefficients of restitution models suited for nonlinear impact behavior in granular systems

Abstract

This study proposes two novel semi-analytical coefficients of restitution (CoR) models to predict nonlinear impact behavior in granular systems. The models address energy loss at the end of the compression phase, redefining a characteristic length to enhance the equation of motion for colliding particles. The first, the inverse CoR model, derives from the inverse collision approach, introducing a length parameter for its analytical solution. The second, the energy CoR model, is proposed by integrating the damping force in conjunction with the energy conservation principles. Both models are semi-analytical since the characteristic length is numerically determined. Despite differing in derivation, both models account for initial impact velocity and material properties. Comparative analysis highlights their advantages over existing models, with validation through experimental data. Simulations confirm that the models yield accurate predictions for both metal and nonmetal contacts, at high and low impact speeds.