Extended Greenwood–Williamson Models for Rough Spheres

Abstract

The current work aims to develop two extended Greenwood–Williamson (GW) models for spherical particles with surface roughness which can be incorporated into the discrete element modeling (DEM) framework. The defects of the classic GW model when directly adopted in DEM are fully addressed and illustrated by both theoretical and numerical results. The first model, the extended elastic GW (E-GW) model, which evaluates the elastic deformation of the asperities and the bulk substrate separately is developed to consider the positive overlap involved in the contact problem. The capability of incorporating the extended elastic model into the DEM is illustrated by the comparison between the classic and extended models. The second model, the extended elasto–plastic GW (EP-GW) model, is further developed to consider the plastic deformation of the asperities which reduces the pressure increased by the surface roughness. Numerical comparisons between the E-GW and EP-GW models are also conducted to demonstrate the effect of the plastic deformation on the pressure and deformation distributions in the contact region.