Computational simulation of crack problems by means of the contour element method

The article discusses a contour element method applied to numerical simulations of crack problems in elastic structures. Because the boundary integral equation degenerates for a body with two crack-surfaces occupying the same location, one of the forms of the displacement discontinuity method is implemented. According to the implemented method, resultant forces and dislocation densities, which are placed at mid-nodes of contour segments on one of the crack surfaces, are characterized by the indirect boundary integral equation. Contrarily to internal crack problems, for edge crack problems an edge-discontinuous element is used at the intersection between a crack and an edge to avoid a common node at the intersection. New numerical formulations that are built up on analytical integration are implemented. Therefore, all regular and singular integrals are evaluated only analytically. Tractions and resultant forces at a mid-node of any contour segment are regularized by a nonlocal characterization function. Hence, values of their components are obtained from the modified form of Somigliana’s identity that embraces nonlocal elements and standard elements of kernel matrices used in the boundary element analysis.