An Analysis of Elastic Rough Contact Models

Abstract

The problem of elastic contact between one nominally flat rough surface and one rigid flat is studied. A variety of contact models have been applied to this problem since the pioneering work of Archard in 1956. Those contact models can be divided into 4 categories namely, the statistical, multi-scale, semi-numerical and deterministic numerical models. In Chapter 1, the methods of describing and generating rough surfaces are introduced. Additionally, the Hertzian contact theory is briefly illustrated. In Chapter 2, the developments of the statistical, multi-scale and semi-numerical models are reviewed briefly by introducing several important models, e.g., the Greenwood-Williamson (GW) model. The contact area to load relations predicted by those models are compared to that by deterministic numerical model (the finite element model) which is treated as the "exact" solution. In Chapter 3 and 4, the developments and applications of two popular deterministic numerical methods namely, the boundary element method (BEM) and the finite element method (FEM), for the elastic rough surface contact are reviewed in detail. The contact area to load relations predicted by the BEM and the FEM are compared. The contact areas and the contact pressure distributions at different stages of deformation are also explored. Conclusions of this study can be drawn in the following aspects: (1) the asperity-based models, e.g., the statistical and semi-numerical models, are only valid for low load condition, (2) the simplified multi-scale model is good for both early contact and complete contact, (3) the contact area to load relations predicted by the FEM and the BEM have very good agreement, at least for the case of isotropic surfaces.