An enriched Scaled Boundary Finite Element Method for 3D cracks

In this work, a direct enrichment approach for the Scaled Boundary Finite Element Method (SBFEM) is proposed and implemented. While the SBFEM has proven its effectiveness in the treatment of 2D boundary value problems with stress singularities, it suffers from reduced convergence rates and accuracy in 3D cases with line singularities. This is due to the then unpreventable occurrence of singularities in the discretized boundary coordinates of the SBFEM. It is shown that enriching the characteristic separation of variables approach of the method directly with the 2D asymptotic near-fields of the line singularities recovers the optimal convergence rates in a uniquely DOF-efficient way. It will also be seen that, at the same time, the presented enrichment approach for the SBFEM can yield a very high accuracy - even for rather coarse discretizations.