The interaction of a curved crack with a circular elastic inclusion

The solution to a curved matrix crack interacting with a circular elastic inclusion is presented. The problem is formulated using the Kolosov–Muskhelishvili complex stress potential technique where the crack is represented by an unknown distribution of dislocations. After an appropriate parameterization, the resulting singular integral equations are solved with the Lobatto-Chebyshev quadrature technique. The accuracy of the current solution is shown by comparing these results to previously published results. A preliminary investigation is conducted to study the effects of crack curvature and inclusion stiffness on the stress intensity factors and it is shown that in certain instances, the effect of the crack curvature and the inclusion stiffness are competing influences.