This paper presents high-order implementations of a generalized finite element method for through-the-thickness three-dimensional branched cracks. This approach can accurately represent discontinuities such as triple joints in polycrystalline materials and branched cracks, independently of the background finite element mesh. Representative problems are investigated to illustrate the accuracy of the method in combination with various discretizations and refinement strategies. The combination of local refinement at crack fronts and high-order continuous and discontinuous enrichments proves to be an excellent combination which can deliver convergence rates close to that of problems with smooth solutions. Copyright © 2007 John Wiley & Sons, Ltd.
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