The problem of an interface crack with a rigid patch plate on part of its edge

A mixed boundary-value problem is solved for a piecewise-homogeneous elastic body with a rectilinear semi-infinite crack on the line where the materials are joined. A rigid patch plate (a reinforcing plate) of specified shape is attached to the upper edge of the crack on a finite interval adjacent to the crack tip. The edges of the crack are loaded with specified stresses. The body is stretched at infinity by a specified longitudinal stress. External forces with a given principal vector and moment act on the patch plate. The problem reduces to a Riemann-Hilbert boundary-value matrix problem with a piecewise-constant coefficient, the solution of which is explicitly constructed using a Gaussian hypergeometric function. The angle of rotation of the patch plate and the complex potentials describing the stress state of the body are found and the stress state of the body close to the ends of the patch plate, one of which is also simultaneously the crack tip, is investigated. Numerical examples are presented that illustrate the effect of the initial force parameters, the length of the patch plate and other parameters of the body on the angle of rotation of the patch plate and the stress state of the body.