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

Contact between an elastic manifold and a rigid substrate with a self- affine fractal surface is reinvestigated with Green's function molecular dynamics. The Fourier transforms of the stress and contact autocorrelation functions are found to decrease as vertical bar q vertical bar- mu where q is the wavevector. Upper and lower bounds on the ratio of the two correlation functions are used to argue that they have the same scaling exponent mu. Analysis of numerical results gives mu = 1 + H, where H is the Hurst roughness exponent. This is consistent with Persson's contact mechanics theory, while asperity models give mu = 2( 1 + H). The effect of increasing the range of interactions from a hard sphere repulsion to exponential decay is analyzed. Results for exponential interactions are accurately described by recent systematic corrections to Persson's theory. The relation between the area of simply connected contact patches and the normal force is also studied. Below a threshold size the contact area and force are consistent with Hertzian contact mechanics, while area and force are linearly related in larger contact patches.