Note on the complete contact between a flat rigid punch and an elastic layer attached to a dissimilar substrate

The contact pressure distribution is found for a square ended rigid punch, pressing normally onto an elastic layer, itself attached to an elastically dissimilar half-plane, under plane deformation. Each interface may be either frictionless or adhesive, and it is shown that the shear traction assumption has only a very small influence on the contact pressure, which is found as a perturbation on the classical Flamant half-plane solution. For thin layers the contact pressure distribution is only weakly dependent on the pad aspect ratio.