Elastic response of rough surfaces in partial contact

We model numerically the partial normal contact of two elastic rough surfaces with highly correlated asperities. Facing surfaces are unmated and described as self-a ne with a Hurst exponent H. The numerical algorithm is based on Fourier acceleration and allows for numerous and large system computations. We find that for H = 0.6 and H = 0.8, the force F scales as A(1.1), where A is the contact area. This is in contrast to the law F similar to A((1+H)/2), predicting an exponent of 0.8 and 0.9, respectively, which was suggested by Roux et al. (Europhys. Lett., 23 (1993) 277). We propose an explanation for this discrepancy.