Overview of three-dimensional linear-elastic fracture mechanics

The aim of this contribution is to provide a brief overview of three-dimensional linear-elastic fracture mechanics (3D LEFM) as well as the latest advances in this area. The primary focus of this review is on the situations where the classical LEFM, which largely relies on plane stress or plane strain simplifications, provides peculiar or misleading results. As no exact analytical solutions are currently available for real cracks, which are inherently three-dimensional (3D), there are many controversial views in the literature and lack of understanding of the effects associated with 3D geometries. Fundamental results and general conclusions in 3D LEFM are largely based on dimensionless and energy considerations as well as on generalisations of outcomes of 3D numerical studies and application of asymptotic techniques. It is believed that 3D considerations alone cannot explain complex and diverse brittle fracture and fatigue phenomena, but these considerations can contribute into the further understanding of these phenomena.