Numerically determined enrichment functions for the extended finite element method and applications to bi‐material anisotropic fracture and polycrystals

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A singular edge-based smoothed finite element method (ES-FEM) for crack analyses in anisotropic media (2011, unknown): “Special treatments [28–34] (e.”
A new generalized finite element method for two‐scale simulations of propagating cohesive fractures in 3‐D (2015, methodology): “This is the basic idea of the GFEMgl [40], the GFEM with mesh-based handbooks [74], the GFEM with numerically defined harmonic enrichment functions [75], the method of Menk and Bordas for fracture of bi-material systems [76], the spider-XFEM [77], and the reduced basis enrichment for the XFEM [78] o”
A two-scale approach for the analysis of propagating three-dimensional fractures (2012, methodology): “Other related methods for two-dimensional static cracks include the spider-XFEM [9] and the reduced basis enrichment for the XFEM of Chahine et al. [10]; the method of Menk and Bordas [ 35 ] for fracture of bi-material systems; the harmonic enrichment functions of Mousavi et al. [39] for two-dimensi”
XFEM fracture analysis of orthotropic functionally graded materials (2013, unknown): “Recently, the automatic enrichment technique has also been developed to numerically determine the required enrichment functions for each problem [47] [48] [49] [50] [51].”