Computing edge singularities in elastic anisotropic three-dimensional domains

Computation of eigen-pairs characterizing the linear elastostatic solution in three-dimensional anisotropic domains in the vicinity of edge singularities is addressed. The singularities may be caused by re-entrant corners, abrupt changes in boundary conditions or material properties. Edge singularities in three-dimensional domains are of great interest from the point of view of failure initiation: The eigen-pairs characterize the straining modes and their amplitudes quantify the amount of energy residing in particular straining modes. For this reason, failure theories directly or indirectly involve the eigen-pairs and their amplitudes. Herein we address the problem of determining the edge eigen-pairs numerically on the basis of the modified Steklov formulation in conjunction with the p-version of the finite element method. The method is very accurate, efficient and robust, and provides complex eigen-pairs if they exist. Several practical problems are studied, and examples are presented for cases including multi-material inclusion problems, cracks in dissimilar materials, and multi-material interfaces at free and clamped edges.