A numerical method with a posteriori error estimation for determining the path taken by a propagating crack Original Research Article

The problem of predicting the path taken by a propagating crack under general loading in a two-dimensional domain is considered. An efficient numerical procedure for computing this path is given and compared to a standard method. The model used to predict the direction of crack growth is the principle of local symmetry. That is, the crack propagates along such a path that the Mode II stress intensity factor is zero along the path. Unlike many methods for computing crack paths, the procedure presented here uses smooth curves to model the crack. The theory behind the method is summarized and an a posteriori error estimate for the difference between the computed crack and the true crack is developed. This allows one to perform an adaptive procedure for finding crack paths. The numerics use a finite element implementation to solve the linear elasticity equations and the contour integral method is used to compute the stress intensity factors.