Local frictional wear of an elastic half-space with a regular system of protrusions

Wear-contact of two elastic half-planes (plain deformation), the surface of one of which has periodic sloping protrusions of cylindrical shape under local wear on the basis of the model of frictional-fatigue fracture is investigated. The formulated contact problem is reduced to a singular integro-differential equation with a Hilbert nucleus with respect to the thickness of the worn material and equations for determining the unknown areas of wear. The shape of the protrusions and contact pressure at the beginning and after wear are analyzed.