On the equilibrium of elastic bodies with weakly curved junction

The work is addressed to the analysis of a boundary value problem with an unknown contact area, which describes equilibrium of two-dimensional elastic bodies with a thin weakly curved junction. It is assumed that the junction exfoliates from the elastic bodies, thereby forming interfacial cracks. Nonlinear boundary conditions of the inequality form are set on the crack faces, excluding the mutual penetration. The unique solvability of the boundary value problem is established. The analysis of limit transitions in terms of the junction stiffness parameter is provided as the parameter tends to infinity and to zero, and limiting models are investigated.