The plane deformable state of piecewise-homogeneous body with defects as open cracks and thin rigid sharp inclusions which locate on the interface of materials is studied. The inclusions perfectly join to the material or they contact with material as a smooth rigid stamp. The complex potentials of composite material and the stress intensity factors near the end-points of the defects are found in explicit form using the Riemann - Hilbert problem on a two-sheeted Riemann surface, and its functional dependence from the elastic parameters of composite material, external forces and forms of the defects is studied.
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