Plane frictional receding contact of a thin layer pressed onto a substrate by finite pressure distributions

A frictional receding contact problem of an infinitely long layer pressed by different finite pressure distributions onto a half-plane of the same linear elastic material is solved with the distributed dislocation technique. Solutions are obtained for when the layer is subject to three different pressure distributions: finite patch of constant pressure, square-root bounded (Hertzian) pressure and square-root singular pressure. The contact tractions, the locations of slip and separation, and the slope of the layer at remote points are found for different coefficients of friction and for different widths of pressure distribution. A universal relationship is deduced between the total slip, the remote slope of the layer and the shear traction.