A study of the representation of cracks with level sets

The level set method has been used for a few years to represent cracks in fracture mechanics simulations instead of an explicit description of the cracks faces geometry. This paper studies in detail the shape of the level set functions around a crack in two dimensions that is propagating with a sharp kink, obtained both with level set update methods found in the literature and with several innovative update methods developed by the author. A criterion based on the computation of a J integral of a virtual displacement field obtained with the values of the level set functions is proposed in order to assess the quality of these update methods. With the help of this criterion, two optimal approaches are identified, which predict an accurate evolution of the crack with smooth and consistent level set functions. These methods are then applied in three dimensions to the case of an initially penny‐shaped crack that propagates out of its plane.