Combined extended and superimposed finite element method for cracks

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A two-scale approach for the analysis of propagating three-dimensional fractures (2012, methodology): “Early methods for the analysis of propagating fractures based on multi-scale concepts include the work of Rashid on the arbitrary local mesh replacement method [51], and several works on the so-called S-method [22, 32].”
Analysis of three‐dimensional fracture mechanics problems: A two‐scale approach using coarse‐generalized FEM meshes (2010, methodology): “Belytschko et al. [9] and the combination of the s-method with the XFEM proposed by Lee et al. [ 42 ] can also be used to solve the class of problems considered in this paper.”
Local enrichment of the finite cell method for problems with material interfaces (2013, background): “This approach is very well suited for problems involving singularities in the exact solution of the underlying problem [45,48].”
A new generalized finite element method for two‐scale simulations of propagating cohesive fractures in 3‐D (2015, methodology): “We mention the S-method [79, 80], the multiscale FEM [81], the multigrid methods proposed in [82, 83], the multiscale methods of Guidault et al.”