PACS. 62.20.Qp -Tribology and hardness. PACS. 68.35.Ct -Interface structure and roughness. PACS. 91.60.Ba -Elasticity, fracture, and flow.Abstract. -We model numerically the partial normal contact of two elastic rough surfaces with highly correlated asperities. Facing surfaces are unmated and described as self-affine 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 ∼ 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.
It is proved that the asymptotic series for the leading term K ∞ (a) of the Keesom integral K(a) obtained by us in a previous paper (2004 J. Phys. A: Math. Gen. 37 9677), in order to evaluate K(a) for large values of the interaction parameter a, is indeed an asymptotic expansion of K(a) itself.
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