Revisit of the equivalence of the displacement discontinuity method and boundary element method for solving crack problems

In this note, it is shown explicitly that the displacement discontinuity method (DDM) is equivalent to the boundary element method (BEM) for solving crack problems. To show this, the direct traction boundary integral equation (BIE) in terms of the displacement jump across crack surfaces is applied to a crack in an infinite 2-D elastic domain. Then, the direct traction BIE is discretized with constant line elements. All the integrals are evaluated analytically. The yielded linear system of equations is found to be exactly the same as the original DDM system of equations in terms of the displacement discontinuities. This proof of the equivalence of the DDM and BEM suggests that the two methods are the same in nature and both are based on the same traction BIE for crack problems.