Dislocation-based boundary-element method for crack problems in anisotropic half-planes

A dislocation-based boundary-element method (BEM) is presented to provide solutions to the crack problems in anisotropic half-planes. The boundary of the half-plane is first modeled by a dislocation array, which is then discretized into boundary elements. Each element is simulated as a continuous dislocation array with linear distribution between the two element nodes. As a result, the singular integral equations derived from the continuous dislocation method for each element can be solved analytically. After the dislocation densities at the element nodes are determined from the prescribed traction forces along the half-plane boundary, the elastic solution of the half-plane can be calculated. Two basic solutions for an anisotropic half plane, that is, traction boundary solution and dislocation solution, are derived and compared with the analytical solutions. These solutions are then applied to solve crack problems in the half-plane subjected to different loading. The results from the dislocation-based BEM are compared with those from the analytical solutions to verify the described BEM. Excellent agreements are achieved for all of the cases.