Edge Stress Intensity Functions in Polyhedral Domains and their Extraction by a Quasidual Function Method

The solution to elastic isotropic problems in three-dimensional (3-D) polyhedral domains in the vicinity of an edge is provided in an explicit form. It involves a family of eigen-functions with their shadows, and the associated edge stress intensity functions (ESIFs), which are functions along the edges. Utilizing the explicit structure of the solution in the vicinity of the edge we use the quasidual function method, recently presented in [Omer et al. (2004). International Journal of Fracture129:97–130] for scalar elliptic problems and in [Costabel et al. (2004). SIAM Journal of Mathematical Analysis35(5), 1177–1202] in a general theoretical framework, for the extraction of ESIFs. This method provides a polynomial approximation of the ESIF along the edge whose order is adaptively increased so to approximate the exact ESIF. It is implemented as a post-solution operation in conjunction with the p-version finite element method. Numerical examples are provided in which we extract ESIFs associated with traction free or homogeneous Dirichlet boundary conditions in 3-D cracked domains or 3-D V-Notched domains. These demonstrate the efficiency, robustness and high accuracy of the proposed quasi-dual function method.