Elastic-plastic Contact of a Rough Surface with Weierstrass Profile

In this appendix, we list the expressions that characterize the response of an elastic-perfectly plastic solid with sinusoidal roughness to indentation by a rigid flat punch. The substrate is an elastic-perfectly plastic solid with Young’s modulus E, Poisson’s ratio ν and yield stress Y σ . The surface roughness has wavelength n λ and amplitude n g . In terms of these parameters, we define a material and geometrical parameter 2 /[(1 ) ] n n n Y g E ψ ν λ σ = − , which characterizes the resistance of the surface to plastic flow. The solid is indented by a flat, rigid surface, under the action of a nominal pressure n p . The loading induces a contact width 2 n a , pressure distribution ( ) n p x and mean pressure mean n p , given by functional relationships