A delaminated inclusion in the case of adhesion and slippage

Abstract

The plane problem of stress concentration near a thin absolutely rigid inclusion is considered. Under the action of a force and a moment, applied to the upper edge of the inclusion, which is completely bonded to an elastic medium, the lower edge of the inclusion separates into layers: a crack opens in a certain inner section and finite slippage zones occur outside it. The problem is equivalent to a system of four singular integral equations in different sections. In the symmetric case, the reduction of this system to a single singular integral equation of the Mellin-convolution type in the interval (μ,1) turns out to be effective, as the latter equation can be solved using a previously proposed scheme [1] as a consequence of the smallness of μ. In the general case, the system is reduced to two Riemann vector problems which are solved successively and for which analytic and asymptotic solutions are constructed. The zones of slippage and detachment, the angle of rotation of the inclusion, the normal displacements of the lower edge of the inclusion and the contact stresses in the slippage zone are found.