Mathematical and numerical aspects of an elasticity-based local approach to fracture

In local approaches to fracture, crack initiation and growth are regarded as the ultimate consequences of a gradual, local loss of material integrity. Standard degradation models, however, are unable to deal with localisation instabilities and the singular strains at the crack tip. As a consequence, finite element analyses become highly sensitive to the spatial discretisation. Adding nonlocal terms to the models enhances their ability to describe fracture processes. An essential role is played by the treatment of the boundary of the equilibrium problem, particularly the internal boundary which represents the crack contour. If the appropriate boundary conditions are applied and the crack region is removed from the discrete equilibrium problem, finite element analyses become mesh-objective.