On the elastic contact of rough surfaces: Numerical experiments and comparisons with recent theories

Some numerical experiments are conducted for studying the decrease of the elastic contact area in the elastic contact of fractal random surfaces when adding components of roughness of progressively smaller wavelengths. In particular, Fourier and Weierstrass random series are used, and a recent accurate and efficient method developed by the authors is used, involving superpositions of overlapping triangles. Some comparisons are made using two recent theories, that of Ciavarella et al. published in 2000 on the deterministic Weierstrass fractal profile, and that of Persson published in 2001 on random generic contact. We show that both theories tend to underpredict the contact area by a significant (and similar) factor in these representative cases in the region of light loads (partial contact), where the non-linearities of the contact mechanics are not included in neither of the formulations. In Persson's theory case, the discrepancy is particularly large at high fractal dimensions of the profile, where in theory the numerical experiments should be more closely reproducing a true Gaussian process. The Ciavarella et al. “Archard-like” theory, is only accurate when the parameter γ (the ratio of successive wavelengths) is unrealistically large. However, we only tested the Ciavarella et al. theory in the simplified “Hertzian approximation” form assuming partial contact at the peaks of contact, although we don’t expect the full version to improve dramatically the results.