The T-stress along a 3-D straight crack. (15th October 2018) - Schapira, Yaron; Omer, Netta; Yosibash, Zohar
Highlights: The asymptotic solution to the elasticity system in the vicinity of an crack in a 3-D domain is provided with emphasis to the T-stress. Having this expansion, and using the quasi-dual function method we extract the T-stress from FE solutions. Numerical examples show the efficiency and accuracy of the methods for the extraction of the edge T-stress. Abstract: The T-stress in a three dimensional elastic domain containing a straight crack is considered. First the complete asymptotic expansion in the vicinity of the crack front, including the T-stress, is presented explicitly. Having obtained the asymptotic expansion, we compute the dual solution associated with the T-stress, and prove it must contain logarithmic terms. This dual solution is used to extend the quasi dual function method (QDFM) for the extraction of the T-stress from finite element solutions and express it as a function along the crack front. Since the stress field tends to infinity at the crack front whereas the T-stress remains constant, its extraction from finite element solutions, containing numerical errors, is a non-trivial task. We herein develop accurate and efficient methods for extracting the T-stress function along the crack edge by the QDFM. Numerical examples are provided for the computation of the T-stresses from conventional and high order finite element methods.