Computing edge stress intensity functions (ESIFs) along circular 3-D edges

A newly developed method, named the quasi-dual function method (QDFM) is proposed for extracting edge stress intensity functions (ESIFs) along circular crack fronts from finite element solutions, in a general three-dimensional domain and boundary conditions. The mathematical machinery developed in the framework of the Laplace operator in [17] is extended here to the elasticity system and applied for the extraction of ESIFs from high-order finite element solutions. The QDFM has several important advantages: a) It allows to extract the ESIFs away from the singular edge, thus avoiding the need for a refined FE mesh, b) The ESIFs are obtained as a function along the edge and not as pointwise values, c) The method is general in the sense that it is applicable to any circular edge (be it a penny shaped crack, a cylindrical crack or a circular external crack). Numerical examples are provided that demonstrate the efficiency, robustness and high accuracy of the proposed QDFM.