On an analytical solution for the damped Hertzian spring

Abstract

Contact models including an elastic and a dissipative force are widely used to model inelastic granular collisions. Whilst there exists an analytical solution for the linear spring-dashpot (LSD) model, for the more practically important non-linear models often only the asymptotic behaviour is known. In this letter, we demonstrate that if the Hertzian contact model is complemented by a damping force proportional to 1/4-power of the normal deformation, it is possible to map its behaviour onto the LSD model and hence obtain simple analytical relationships between the model parameters and the characteristics of the granular collision. In practice, this allows the prediction of parameters for discrete element models of powder flow and compaction by using experimental observables such as restitution coefficient and collision time as input data.