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A decade after its introduction, the extended finite element method (XFEM) has now become an usefull numerical approach for analysis of crack propagation problems. In the XFEM, a standard displacement based finite element approximation is enriched by additional functions using the framework of partition of unity. Besides, the finite element mesh need not conform to the internal boundaries (cracks, material interfaces, voids, etc.), and hence a single mesh suffices for modeling as well as capturing the evolution of material interfaces and cracks. The striking advantages are that the finite element framework (sparsity and symmetry of the stiffness matrix) is retained.
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 Asadpoure A, Mohammadib S, Vafai A. Crack analysis in orthotropic media using the extended finite element method. Thin-Walled Structures, 2006, 44:1031-1038.
 Dumstorff P, Meschke G. Crack propagation criteria in the framework of X-FEM-based structural analyses. International Journal for Numerical and Analytical Methods in Geomechanics, 2007, 31:239-259.
 Abdelaziz Y, Hamouine A. A survey of the extended finite element. Computers and Structures, 2008, 86:1141-1151.
 Fries T P, Belytschko T. The extended/generalized finite element method: an overview of the method and its applications. International Journal for Numerical Methods in Engineering, 2010, 84: 253-304.
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