Asymptotic analysis of a delamination in a bi-layered plate

The problem of the static deformation of a bi-layered plate with a crack is considered. The crack is placed at the interface and has arbitrary shape in the plan view. A system of integro-differential equations for the crack opening is obtained. With the assumption that the plate thickness is much smaller than the crack scale, the asymptotic inner and outer problems are introduced. The inner problem is the 2-D one of the semi-infinite crack in the bi-material strip. The outer problem is that of the deformation of two plates clamped along the crack contour with the boundary conditions determined by the solution of the inner problem. Matching solutions of the inner and outer problems leads to the formulae for the stress intensity factors.