Contact problem for interfacial exfoliated inclusion

The equilibrium of two rigidly connected elastic half-planes made of different materials, with a thin rigid inclusion placed on the border of their separation, is considered. One side of the inclusion is connected to one of the half-planes, and the other is exfoliated with the formation of a crack. The frictional contact of the crack faces near its tips is taken into account. Using the Wiener–Hopf method, the solution of the system of integral equations of the problem is obtained in a closed form. The dimensions of the areas of contact of the crack faces, stress distributions in the areas of contact, at the boundary of the separation of the half-planes outside the crack and at the junction of the inclusion with the half-plane, asymptotic distributions of stresses and displacements in the vicinity of the end of the inclusion were found.