In this paper, the modified or corrected extended finite element method originally presented in Fries (Int. J. Numer. Meth. Engng. 2008; 75:503–532) for the 2D case is extended to 3D including different remedies for the problem that the crack front enrichment functions are linearly dependent in the blending elements. In the context of this extension, we address a number of computational issues of the 3D XFEM, in particular possible quadrature rules for elements with discontinuities. Also, the influence of finite deformation theory for crack simulations in comparison to linear elastic fracture mechanics is investigated. A number of numerical examples demonstrate the behavior of the presented possibilities. Copyright © 2010 John Wiley & Sons, Ltd.
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