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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.

In this paper we describe a new enhanced assumed strain finite element for finite deformations. The element is based on the split of the deformation of an element into a homogeneous and inhomogeneous part. The enhancement is applied to the inhomogeneous part only. For the homogeneous part a compressible Neo-Hooke material is used, while for the inhomogeneous part linear elasticity is assumed. In several examples it is shown that the element is locking and hourglassing free as well as insensitive to initial element distortion. Copyright © 2008 John Wiley & Sons, Ltd.