Contact mechanics of rough spheres: Crossover from fractal to Hertzian behavior

Abstract

We investigate the normal contact stiffness in a contact of a rough sphere with an elastic half-space using 3D boundary element calculations. For small normal forces, it is found that the stiffness behaves according to the law of Pohrt/Popov for nominally flat self-affine surfaces, while for higher normal forces, there is a transition to Hertzian behavior. A new analytical model is derived describing the contact behavior at any force. © 2013 Roman Pohrt and Valentin L. Popov.