antiplane shear, crack, piecewise-homogeneous body, matrix Riemann-Hilbert problem, stress intensity factors.

Antiplane stress state of a piecewise-homogeneous elastic body with a semi-infinite crack along the interface is considered. The longitudinal displacements along one of the crack edges on a finite interval, adjacent to the crack tip, are known. Shear stresses are applied to the body along the crack edges and at infinity. The problem reduces to a Riemann-Hilbert boundary- value matrix problem with a piecewise-constant coefficient for a complex potential in the class of symmetric functions. The complex potential is found explicitly using a Gaussian hypergeometric function. The stress state of the body close to the singular points is investigated. The stress intensity factors are determined.

1. Silvestrov Vasiliy Vasilyevich, Doctor of Physical and Mathematical Sciences, Professor of the Department of Mathematics, Russian State University of Oil and Gas, Moscow, Russia. 2. Urakova Iuliia Olegovna, Candidate of Physical and Mathematical Sciences, Lecturer of the Department of Actuarial and Financial Mathematics, Chuvash State University, Cheboksary, Russia. 3. Ilina Irina Igorevna, Candidate of Physical and Mathematical Sciences, Chuvash State University, Cheboksary, Russia.