A NUMERICAL-METHOD WITH A-POSTERIORI ERROR ESTIMATION FOR DETERMININGTHE PATH TAKEN BY A PROPAGATING CRACK

The problem of predicting the path taken by a propagating crack under general loading in a two-dimensional domain is considered. An efficien t numerical procedure for computing this path is given and compared to a standard method. The model used to predict the direction of crack g rowth is the principle of local symmetry. That is, the crack propagate s along such a path that the Mode II stress intensity factor is zero a long the path. Unlike many methods for computing crack paths, the proc edure presented here uses smooth curves to model the crack. The theory behind the method is summarized and an a posteriori error estimate fo r the difference between the computed crack and the true crack is deve loped. This allows one to perform an adaptive procedure for finding cr ack paths. The numerics use a finite element implementation to solve t he linear elasticity equations and the contour integral method is used to compute the stress intensity factors. (C) 1998 Elsevier Science S. A. All rights reserved.