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

Zohar Yosibash (1) , Netta Omer (1) , Martin Costabel (2) , Monique Dauge (2)

1 Department of Computer Science [Beer-Sheva]
2 IRMAR - Institut de Recherche Mathématique de Rennes

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, the theoretical fundation of which is due to a former work by MC, MD and ZY. 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.

Domaines: Analyse numérique [math.NA]; Mécanique des structures [physics.class-ph]; Mécanique des structures [physics.class-ph]

Zohar Yosibash, Netta Omer, Martin Costabel, Monique Dauge. Edge Stress Intensity Functions in Polyhedral Domains and their Extraction by a Quasidual Function Method. International Journal of Fracture, 2005, 136 (1-4), pp.37--73. ⟨hal-00012184⟩