The solution to elastic isotropic problems in three-dimensional (3-D) polyhedral domains has an explicit structure in the vicinity of the edges. This structure involves a family of eigen-functions with their shadows, and the associated Edge Stress Intensity Functions (ESIFs), which are functions along the edges.

For the extraction of ESIFs, we apply the Quasidual Function Method, already presented in OmYoCoDa04 for scalar elliptic problems and in
CoDaYo04 in a general theoretical framework.

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.

May 2005.

International Journal of Fracture Vol. 136, N° 1-4 (2005), pp 37-73.

Pdf file (1200 k)