We study the nominal (ensemble averaged) contact pressure $p(x)$ acting on a cylinder squeezed in contact with an elastic half-space with random surface roughness. The contact pressure is Hertzian-like for $\alpha < 0.01$ and Gaussian-like for $\alpha > 10$, where the dimensionless parameter $\alpha = h_{ \rm rms}/\delta$ is the ratio between the root-mean-square roughness amplitude and the penetration for the smooth surfaces case (Hertz contact).
Categories: cond-mat.soft cond-mat.mtrl-sci cond-mat.stat-mech