On the construction of blending elements for local partition of unity enriched finite elements

By J. Chessa, Hongwu Wang, Ted Belytschko. 2003

369 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/92f0ef1f006f30f12a795c7127050dae1186856f

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In Mechanics of Materials

Citations in the corpus

Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment (2008, neutral): “The discontinuous part of the displacement approximation due to crack a 2 E writes 8X 2 X0; 8t > 0; ueaðX; tÞ ¼ X I2Wa UIðXÞWaI ðXÞaaI ðtÞ ð8Þ Note that the shape functions UI in Eq.”
A posteriori error estimation for extended finite elements by an extended global recovery (2008, background): “Note that our error estimator naturally captures the blending error, due to the mismatch between different partitions of unities at the interface of the enriched domain and is now well known in the context of the XFEM [39, 40, 42], and recent work [43], where an assumed strain element is proposed to”
Combined extended and superimposed finite element method for cracks (2004, background): “[13] pointed out that a local partition of unity loses the reproducing property in the region where the enriched elements are blended with standard finite elements.”
A Meshfree Method based on the Local Partition of Unity for Cohesive Cracks (2007, neutral): “[18].”
An extended finite element method for fluid flow in partially saturated porous media with weak discontinuities; the convergence analysis of local enrichment strategies (2013, methodology): “This issue has already been addressed in applications to weak discontinuities and a number of techniques have been developed to overcome the drawback caused by the blending elements [30–36].”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, neutral): “We also discuss blending elements (elements that have partially enriched nodes) (Chessa et al. 2003) and the use of shifted enrichment functions.”
Multiscale enrichment based on partition of unity (2005, methodology): “In XFEM, which use local partition of unity [ 45 ], the enrichment functions are used to describe spatial features, such as asymptotic crack fields [33] or local flow fields [46]; in addition they provide means to model arbitrary discontinuities.”
Blending in the extended finite element method by discontinuous Galerkin and assumed strain methods (2008, methodology): “[10] with an AS formulation for the blending elements, and it was shown that AS-XFEM gives the exact result.”
Strong and weak arbitrary discontinuities in spectral finite elements (2005, methodology): “Engng 2005; 64:991–1008 in the blending elements, we use the assumed strain method to project out these strains as in Reference [7].”