Problem of a thin rigid inclusion inserted in an interfacial crack in the vicinity of its tip

The problem of the stress state of a piecewise-homogeneous elastic body with a semi-infinite crack at an interface, in which near the vertex inserted a thin rigid pointed inclusion of finite length. The crack faces are loaded by predetermined stresses, and at infinity, the body is stretched by predetermined normal stresses acting along the crack. The inclusion is acted upon by external forces that have predetermined main vector and moment. The problem reduces to the matrix Riemann boundary-value problem with a piecewise constant coefficient. The solution of this problem is constructed in explicit form using the Gauss hypergeometric function. The angle of rotation of the inclusion, complex potentials, and stress intensity factors near the ends of the inclusion are obtained.