Abstract
A method for solving problems of fracture of an infinite solid with a circular cylindrical cavity and a coaxial cylindrical crack near the surface under an uniform axial compression is proposed using a non-classical criterial approach associated with a mechanism of a local stability loss near the defect. The theory of integral Fourier transforms and series expansions are used to reduce these problems to a system of paired integral equations and then to a system of linear algebraic equations with respect to the contraction parameter.
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