Abstract
Non-axisymmetric frictionless JKR-type adhesive contact between a rigid body and a thin incompressible elastic layer bonded to a rigid base is considered in the framework of the leading-order asymptotic model, which has the form of an overdetermined boundary value problem. Based on the first-order perturbation of the Neumann operator in the Dirichlet problem for Poisson's equation, the decohesion initiation problem is formulated in the form of a variational inequality. The asymptotic model assumes that the contact zone and its boundary contour during the detachment process are unknown. The absence of the solvability theorem is illustrated by an example of the instability of an axisymmetric flat circular contact.