Elastic contact between self-affine surfaces: comparison of numerical stress and contactcorrelation functions with analytic predictions

Abstract

Contact between an elastic manifold and a rigid substrate with a self-affine fractalsurface is reinvestigated with Green’s function molecular dynamics. The Fouriertransforms of the stress and contact autocorrelation functions are found to decrease as|q|−μ where q is the wavevector. Upper and lower bounds on the ratio of the two correlationfunctions are used to argue that they have the same scaling exponentμ. Analysis ofnumerical results gives μ = 1+H, where H is the Hurst roughness exponent. This is consistent with Persson’s contact mechanics theory, while asperitymodels give μ = 2(1+H). The effect of increasing the range of interactions from a hard sphere repulsion toexponential decay is analyzed. Results for exponential interactions are accurately describedby recent systematic corrections to Persson’s theory. The relation between thearea of simply connected contact patches and the normal force is also studied.Below a threshold size the contact area and force are consistent with Hertziancontact mechanics, while area and force are linearly related in larger contactpatches.