Generalized displacement correlation method for estimating stress intensity factors

Conventional displacement-based methods for estimating stress intensity factors require special quarter-point finite elements in the first layer of elements around the fracture tip and substantial near-tip region mesh refinement. This paper presents a generalized form of the displacement correlation method (the GDC method), which can use any linear or quadratic finite element type with homogeneous meshing without local refinement. These two features are critical for modeling dynamic fracture propagation problems where locations of fractures are not known a priori. Because regular finite elements’ shape functions do not include the square-root terms, which are required for accurately representing the near-tip displacement field, the GDC method is enriched via a correction multiplier term. This paper develops the formulation of the GDC method and includes a number of numerical examples, especially those consisting of multiple interacting fractures. We find that the proposed method using quadratic elements is accurate for mode-I and mode-II fracturing, including for very coarse meshes. An alternative formulation using linear elements is also demonstrated to be accurate for mode-I fracturing, and acceptable mode-II results for most engineering applications can be obtained with appropriate mesh resolution, which remains considerably less than that required by most other methods for estimating stress intensities.