A contact model for elastic-plastic rough spheres

The contact of rough spheres is critical in many fields, yet analyzing the effects of roughness and plasticity on the load-area relation is challenging. This paper presents a model for rough elastic-plastic spheres in contact with a rigid plane. Using finite element simulations, we derive an explicit expression for contact pressure in smooth elastic-plastic spheres. For rough spheres, the local load is estimated from this expression, and the local real contact area is determined by the contact behavior of nominally flat elastic-plastic solids, which is established for whole-range using finite element method. By integrating across the contact region, the total real contact area is calculated. The model aligns well with finite element and experimental results, confirming its accuracy and applicability.