Laminate structures composed of fibre-reinforced plies typically are prone to the formation of inter-fiber cracks because of the given strongly anisotropic stiffness and strength properties. These inter-fiber cracks commonly run through complete plies but are stopped at the ply interfaces. Equally, such laminate structures are prone to the formation of delaminations, e.g. due to the free-edge effect. An inter-fiber crack meeting a delamination forms a non-standard three-dimensional crack configuration with a locally singular stress field that should be investigated in regard of its criticality.

For that purpose, the Scaled Boundary Finite Element Method turns out to be an appropriate and effective analysis method that permits solving linear elastic mechanical problems including stress singularities with comparably little effort. Only the boundary is discretized by two-dimensional finite elements while the problem is considered analytically in the direction of the dimensionless radial coordinate ξ. A corresponding separation of variables representation for the displacement field employed in the virtual work equation leads to a system of differential equations of Cauchy-Euler type. This differential equation system can be converted into an eigenvalue problem and solved by standard eigenvalue solvers for non-symmetric matrices.

By this kind of analysis, it is revealed that the considered three-dimensional crack configurations may go along with various unexpected non-standard stress singularities, namely singularities that are weaker than the well-known square root stress singularity in linear elastic fracture mechanics, but also singularities that are stronger and which may be called hypersingularities.