Abstract
The problem of the elastic contact of nominally flat surfaces is reviewed towards the mathematical derivation of the resultant contact stiffness in terms of the surface topographies. The present study puts forth two approaches based on the elementary theories of elastic contact. When considering the theory of Greenwood and Williamson (GW model), it is found that the contact stiffness is dependent upon the standard deviation of height distribution of asperities, the effective radius of curvature of asperities and the density of asperities per unit area. When considering the theory of Onions and Archard (OA model), the contact stiffness is found to be dependent upon the correlation distance, the apparent area of contact and the standard deviation of height distribution of asperities. However, it is found that the standard deviation in both models strongly affects the value of contact stiffness. Moreover, the variation of contact stiffness with normal load is similar to that of a stiffening spring. It is also shown that the GW model underestimates the contact stiffness when it is compared with the OA model.