Edge singularities in 3-D elastic anisotropic and multi-material domains

Abstract

The solution to elasticity problems in three-dimensional (3-D) polyhedral multi-material anisotropic domains in the vicinity of an edge is addressed. It includes eigen-functions (similar to 2-D domains) complemented by shadow-functions and their associated edge stress intensity functions (ESIFs), which are functions along the edge. These can be complex and are of major engineering importance in composite materials because failure theories directly or indirectly involve them. The p-version finite-element methods presented in Yosibash and Omer [Z. Yosibash, N. Omer. Numerical methods for extracting edge stress intensity functions in anisotropic three-dimensional domains. Comput. Methods Appl. Mech. Engrg., 196 (2007) 3624–3649] are extended herein to compute complex eigen-functions and shadows and applied to multi-material anisotropic interfaces. The quasidual function method [M. Costabel, M. Dauge, Z. Yosibash. A quasidual function method for extracting edge stress intensity functions. SIAM J. Math. Anal. 35(5) (2004) 1177–1202] is also extended for extracting complex ESIFs from finite element solutions. Numerical examples for 3-D isotropic and anisotropic multi-material interfaces are provided for which the complex eigen-pairs and shadow functions are numerically computed and ESIFs extracted. These examples show the efficiency and high accuracy of the numerical approximations.