High‐order extended finite element method for cracked domains

By P. Laborde, Julien Pommier, Yves Renard, Michel Salaün. 2005

482 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f36533650a98953786680e1008b1d5bf318972ad

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Isogeometric analysis: An overview and computer implementation aspects (2012, unknown): “, [128].”
An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks (2015, methodology): “However, the XFEM/GFEM is accompanied with the challenging issue of ill-conditioned or even singular system matrix [3, 29, 60], reducing the convergence rate of an iterative solution scheme or causing severe loss of digits in a direct method.”
Extended virtual element method for the Laplace problem with singularities and discontinuities (2019, methodology): “This sub-optimal convergence was also noted in previous finite element studies where enrichment for crack problems (λ = 1/2) is used [34].”
Optimal convergence analysis for the extended finite element method (2011, methodology): “This important sensitivity to the shape of the cut-off function suggests to investigate in the future the variant with a pointwise matching [25] or an integral matching [15, 11] which avoid the use of a cut-off function.”
A high‐order generalized FEM for through‐the‐thickness branched cracks (2007, unknown): “[25].”
A review of extended/generalized finite element methods for material modeling (2009, methodology): “The effects of the size of the crack tip enrichment domain has been studied by Ventura et al. [109], Laborde et al. [64] and Béchet et al. [8].”
Strain smoothing in FEM and XFEM (2010, background): “Tip elements either contain the tip, or are within a fixed distance, renr of the tip, if geometrical enrichment is used [10,49].”
Extended finite element method with global enrichment (2015, methodology): “[23] and other similar works [25,47] to three dimensional crack propagation problems, a goal which is not straight forward.”
A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics (2013, background): “2 of [24]).”
Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (2010, methodology): “The singular integrand over the standard triangle is transformed into a smooth function over the unit square that can be integrated with fewer integration points [58, 60], e.”