Improved implementation and robustness study of the X‐FEM for stress analysis around cracks

By Eric Béchet, Hans Minnebo, Nicolas Moës, B. Burgardt. 2005

461 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ce691d1166994982dfa6cd28130b3a71eacf6e21

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

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”
Integration of singular enrichment functions in the generalized/extended finite element method for three‐dimensional problems (2009, methodology): “…q 2008 John Wiley & Sons, Ltd. Received 12 August 2008; Revised 30 October 2008; Accepted 17 November 2008 KEY WORDS: GFEM/X-FEM; BEM; weakly singular integration; mapping method; branch functions; generalized FEM; extended FEM; boundary element method; fracture; singular enrichment functions”
Accurate recovery-based upper error bounds for the extended finite element framework (2010, methodology): “1) as proposed in [7,8] to improve the convergence rate of the XFEM solution.”
The extended finite element method for fracture in composite materials (2009, background): “Although this causes no problems for strong discontinuities, for the weak discontinuities at material interfaces and for crack tip enrichments, it requires blending that degrades accuracy slightly [21, 22].”
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 isogeometric analysis for simulation of stationary and propagating cracks (2012, background): “of selection of enriched control points, sometimes called topological enrichment, one may apply geometrical enrichment [21] in which the area of enrichment remains constant in the refinement process or order elevation.”
Mass lumping strategies for X‐FEM explicit dynamics: Application to crack propagation (2008, methodology): “The implementation of the X-FEM requires some enhancements of the regular FEM implementation: • A specific integration scheme on elements whose nodes are enriched must be used [4, 10].”
Derivative recovery and a posteriori error estimate for extended finite elements (2007, methodology): “This corroborates the findings of References [23, 9].”
Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling (2011, methodology): “The LSM was first applied to crack modelling using the XFEM in [20].”
Generalized Gaussian Quadrature Rules for Discontinuities and Crack Singularities in the Extended Finite Element Method (2010, background): “Here, we generalize the algorithm in Reference [36] to develop quadrature rules for piecewise polynomials on finite elements that are intersected by kinked cracks.”
A mixed augmented Lagrangian‐extended finite element method for modelling elastic–plastic fatigue crack growth with unilateral contact (2007, unknown): “Engng 2007; 71:1569–1597 DOI: 10.1002/nme In previous work (References [19, 20]) the method has shown its ability to obtain accurate results in confined plasticity for the J integral and the stress intensity factors with a relatively coarse mesh.”
A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics (2013, background): “In this socalled geometrical enrichment [6, 24], the size of the enrichment zone is independent of the mesh size, in contrast with the topological enrichment [6, 24].”