Mixed antiplane boundary‐value problem for a piecewise‐homogeneous elastic body with a semi‐infinite interfacial crack

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. Copyright © 2016 John Wiley & Sons, Ltd.