Statistical Characteristic in Contact Response of Random Rough Surface

Abstract This study investigates the statistical characteristics in the contact response of a self-affine rigid rough surface with an isotropic elastic half-space, utilizing a customized boundary element method. Although existing theoretical models predict a linear relationship between real contact area and normal load, the proportionality is often treated as a deterministic constant depending on the root mean square slope of the rough surface. In the present study, numerous simulations are conducted on various sets of random rough surfaces with the ratio of the surface length to the longest wavelength varying from 1 to 16, the ratio of the longest to the shortest wavelength ranging from 8 to 128, and the Hurst exponent spanning 0.3 to 0.9, and each set contains 300 realizations with the same power spectral density. First, it is revealed that the proportionality between real contact area and load is inherently random and follows a Gaussian distribution. The influence of morphological parameters on the mean and variance of the proportionality is addressed, and the dependence of the mean value on the ratio of upper to lower wavenumber and Hurst exponent is presented analytically. By introducing a probabilistic perspective to rough contact mechanics, the work provides insights that can enhance both theoretical modeling and practical design of rough interfaces in sealing, friction, and load-bearing performance.