Stochastic Discrete Element Modelling of Rough Particles

Particles are assumed smooth in classical discrete element modelling, but real particles have random rough surfaces which may influence their mechanical properties. It is necessary therefore to quantitatively improve the conventional discrete element model by taking the surface roughness into consideration. In this work, a new normal contact law is established for particles that have random rough surfaces. The contact law, based on the classic Greenwood and Williamson (GW) model, is derived by both theoretical derivation and numerical calculations. Instead of a complicated integral expression involved in the GW model, the resulting empirical formula of the law retains the closed form and simplicity of the Hertzian model, with only one added parameter, σ, the standard derivation of a surface roughness, and therefore can be readily incorporated into the current discrete element modelling framework.