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-affine with a Hurst exponent H . The numerical algorithm is based on Fourier acceleration and allows efficient simulation of very large systems. The force, F , versus contact area, A, characteristics follows the law F ∼ A in accordance with the suggestion of Roux et al. (Europhys. Lett. 23, 277 (1993)). However finite size corrections are very large even for 512×512 systems where the effective exponent is still 20% larger than its asymptotic value. The mechanical properties of bodies in contact have been studied for a long time [1] since they have important applications ranging from the flow properties of powders to earthquake dynamics [2]. For example, frictional properties are related to the normal stresses that develop during contact, and they have recently been shown to be very sensitive to heterogeneities in the normal stresses [3]. On the fault scale, the dynamical stress field, which is responsible for earthquakes, is strongly influenced by heterogeneities due to asperity squeeze [4]. In this letter we investigate numerically the elastic response of self-affine rough surfaces that are squeezed together. The rough surface, which we take to be oriented in the (x, y) plane, is given by z = z(x, y). If p(z;x, y) is the probability density to find the surface at a height z at (x, y), self affinity is the scaling property λp(λz;λx, λy) = p(z;x, y) , (1) where H is the Hurst or roughness exponent [5,6]. There is strong experimental evidence that surfaces resulting from brittle fracture are self affine with a Hurst exponent equal to 0.8 [7–12]. When two elastic media are forced into contact along two non-matching self-affine rough surfaces, two mechanisms conspire to produce a power law dependence of the applied normal