On elastic-plastic normal contact force models, with and without adhesion

Abstract

The simple problem of the normal impact of a sphere with a target wall is used to evaluate various elastic-plastic normal contact force models reported in the literature. Both non-adhesive and adhesive contact force models are considered, including both models based on contact mechanics theory and other simpler models frequently used in Discrete Element Modelling (DEM). In the context of non-adhesive, elastic perfectly plastic interactions involving idealised spheres, it is demonstrated that, for piecewise linear models, a variable unloading stiffness needs to be scaled to the square root of the maximum relative approach, in order to obtain a realistic velocity dependency of the coefficient of restitution. In the case of elastic perfectly plastic adhesive interactions of spherical particles, it is demonstrated that some existing models are unphysical and lead to qualitatively wrong dependencies of the coefficient of restitution on the magnitude of the impact velocity.