Asymptotic modeling of the JKR adhesion contact for a thin elastic layer

The Johnson--Kendall--Roberts model of frictionless adhesive contact is extended to the case of a thin transversely isotropic elastic layer bonded to a rigid base. The leading-order asymptotic models are obtained for both compressible and incompressible elastic layers. The boundary conditions for the contact pressure approximation on the contour of the contact area have been derived from the boundary-layer solutions, which satisfy the condition that the stress intensity factor of the contact pressure density should have the same value all round the contact area boundary. In the incompressible case, a perturbation solution is obtained for a slightly perturbed circular contact area.