Approximation schemes of stresses on elements for the three-dimensional displacement discontinuity method

The displacement discontinuity method is a boundary element method. It uses the analytical expressions for displacements and stresses in an infinite isotropic homogeneous linear elastic body caused by difference (discontinuity) of displacements across small planar crack surfaces. The basic solution of the method is the displacement discontinuities (DDs) across the crack elements. After DDs are obtained, the displacement and stresses at other points in the body can be calculated. It discretises the crack without considering the individual surface of the crack, thus for crack propagation issues, it uses fewer (half) number of elements than normal BEM and therefore less computation time and computer memory requirement. However, it is found that the stresses calculated from the DDs for points on and close to the crack have large errors. Here we present two numerical schemes for approximation of stresses on the crack elements in three-dimensional problems, which are implemented in a code for fracture propagation. The schemes give a reasonably accurate approximation for elements where the crack surface is relatively smooth. It is found that for elements next to sharp kinking or at the corner of a crack, the results from the schemes are not satisfactory. A modification is proposed for these cases.