On the displacement discontinuity method and the boundary element method for solving 3-D crack problems

In this paper, it is shown that the equations of the displacement discontinuity method (DDM) for solving 3-D crack problems are exactly the same as the equations of the boundary element method (BEM) based on the boundary integral equation (BIE). Therefore, many of the results in the BEM research can be applied directly to the DDM, such as the results of analytical integration and fast solution methods, due to this equivalence or connection. A couple of examples are presented to show the accuracy of the DDM or the BEM with constant triangular elements in solving 3-D problems, when the analytical integration results are applied. It is concluded that the DDM can be applied to solve more complicated 3-D crack problems, such as interaction of multiple cracks and cracks with curved surfaces, with high accuracy and efficiency if the techniques available in the BEM are adopted.