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procedure for the determination of stress intensity factors of 3D flat cracks is proposed, which uses integral identities for displacements and strains on the crack surface. New formulations of boundary problems of the mathematical theory of linear fracture mechanics have been obtained, which are used to develop finite element models. The unknown functions are nodal displacements on the crack surface. The data given are compared with analytical solutions and results obtained by other methods. [ABSTRACT FROM AUTHOR]

We propose new representations of displacements, relative changes in the volume, and angles of rotation of points of a linearly elastic body via the displacements and stresses specified on its surface and deduce integral representations of the boundary conditions for a half space and plane mathematical cuts of any shape. Integral equations for displacements of the surfaces of these cuts are constructed and the results of their solution aimed at finding the stress intensity factors for three-dimensional cracks are analyzed. The proposed relations are compared with the well-known analytic and numerical solutions of the problems of fracture mechanics. [ABSTRACT FROM AUTHOR]