Anisotropic Elasticity and Multi-Material Singularities

Multi-material wedges associated with convergence of geometrical and material discontinuity lines generally show singular stress fields around the vertex of the wedge. In this paper, the eigenvalue problem for a multi-material wedge composed of several anisotropic elastic sectors is formulated in a completely generally manner, including the cases of degenerate and extra-degenerate material sectors, and various types of edge conditions for both open and closed wedges. General representation of the elasticity solution in a degenerate or extra-degenerate anisotropic sector requires higher-order eigenmodes (generalized eigenfunctions) in addition to zeroth-order eigenmodes. Such higher-order eigenmodes are obtained from appropriate analytical expressions of the zeroth-order eigenmode by using the derivative rule. The analysis is applied to one bisector wedge and one trisector wedge in a three-layer cracked composite model to obtain accurate elasticity solutions of the singular stress fields. These solutions were determined using the traction data generated on a circular collocation path by a conventional finite element analysis.