A modified Greenwood–Williamson contact model with asperity interactions

Accurate relation between load and area is of great interest in tribology, especially for large contact fraction, in which the asperity interactions play an import role. The constant mean contact radius obtained in the original Greenwood–Williamson model is adopted in this work; Then, the asperity interactions are dealt with by arranging the random distributed contact spots to hexagon distribution. Finite element simulation is employed to consider only a representative unit with symmetrical boundary conditions, and the corresponding load-area relation is determined up to almost complete contact. For a given contact fraction, interactions induce larger load compared to the GW model without asperity interactions. Furthermore, by comparing with the analytical result given by an incremental contact for small contact fraction, the obtained load-area relation is extended to a general formulation, which shows good agreement with direct finite element simulations. The obtained relations are more general and applicable for a large range of contact fraction. This model provides an efficient method to predict the overall contact response of rough surfaces and reduces the computational burden greatly.