Using Green's function molecular dynamics to rationalize the success of asperity models when describing the contact between self-affine surfaces.

We use Green's function molecular dynamics to evaluate the effectiveness of asperity models when describing the contact mechanics of elastic solids with self-affine surfaces. Surfaces are created with the help of a Fourier filtering algorithm, and the interactions between the solids are modeled via hard-wall potentials. We illustrate how the real area of contact A_{real} is formed by a set of contact clusters. Two different regimes are identified when the normal force per cluster L_{c} is plotted as a function of its area A_{c} . Small clusters satisfy a Hertzian-type law L_{c} approximately A_{c};{32} , while large clusters display a linear L_{c} approximately A_{c} behavior. It is shown how the area A_{c};{*} , where the crossover between the two regimes takes place, depends only on the roughness at the smallest length scale if the longitudinal dimension of the surface remains unaltered. Moreover, our results display a distribution of cluster sizes P(A_{c}) remaining nearly constant for areas smaller than A_{c};{*} , while showing power law decay above such a critical value. Furthermore, we found the heights of the contacting atoms to be normally distributed with width inversely proportional to the surface roughness.