A hybrid analytic-numerical method for three-dimensional cracks

This paper applied a hybrid analytic and numerical method to determine the displacement field and stress intensity factors of cracks in a three-dimensional (3D) body. First, an analytic solution including primary and shadow solutions of a semi-infinite crack in a 3D elastic body was developed, where the primary solutions are the traditional plane-strain solutions and the shadow ones are based on the 3D equilibrium equation. Only the multiplying factors of these solutions need to be determined, and they are constant in each plane perpendicular to the crack surface. A least-squares method incorporating the finite element results was used to determine these factors. If enough primary and shadow solutions are included, the proposed method can obtain an accurate displacement field for 3D crack problems. The major advantage of this method is that a 3D whole displacement field with the analytic singular effect near the crack tip can be obtained.