An overview of a hybrid crack element and determination of its complete displacement field

The hybrid crack element (HCE) is one of the most accurate and convenient finite elements for the direct calculation of the stress intensity factor (SIF) and coefficients of the higher order terms of the Williams expansion. It is formulated from a simplified variational functional using truncated asymptotic crack tip displacement and stress expansions and interelement boundary displacements compatible with the surrounding regular elements. However, the exclusion of the rigid body modes in the truncated asymptotic displacements creates jumps between these displacements and element compatible boundary displacements. In this study, an overview of the HCE is given. Furthermore, the rigid body modes excluded in its formulation are recovered by minimizing the jumps via a least squares method. Limitations of the boundary collocation method (BCM) widely used for predicting these terms, as well as the complete displacements are also investigated.