Arbitrary branched and intersecting cracks with the eXtended Finite Element Method

By Christophe Daux, John Dolbow, Natarajan Sukumar, Ted Belytschko. 2000

1,051 citations recorded by the source corpus.

SUMMARY Extensions of a new technique for the nite element modelling of cracks with multiple branches, multiple holes and cracks emanating from holes are presented. This extended nite element method (X-FEM) allows the representation of crack discontinuities and voids independently of the mesh. A standard displacementbased approximation is enriched by incorporating discontinuous elds through a partition of unity method. A methodology that constructs the enriched approximation based on the interaction of the discontinuous geometric features with the mesh is developed. Computation of the stress intensity factors (SIF) in dierent examples involving branched and intersecting cracks as well as cracks emanating from holes are presented to demonstrate the accuracy and the robustness of the proposed technique. Copyright ? 2000 John Wiley & Sons, Ltd.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/5137d59265fc873a22c0ebee67ca48e09e9d088d

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

A comparative study on the modelling of discontinuous fracture by means of enriched nodal and element techniques and interface elements (2009, methodology): “Here, in both the DSDA and the GFEM, only one discontinuity is allowed in each parent finite element; however, both formulations can be extended to include multiple discontinuities (Dias-da-Costa et al. 2009; Daux et al. 2000; Simone et al. 2006).”
A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries (2006, methodology): “With reference to Figure 5(b), the counting of degrees of freedom equals 28 for both XFEM [7] and GFEM approximations.”
MODELING QUASI-STATIC CRACK GROWTH WITH THE EXTENDED FINITE ELEMENT METHOD PART II: NUMERICAL APPLICATIONS (2003, methodology): “The methodology adopted for modeling crack discontinuities falls within the purview of the X-FEM (Mo€es et al., 1999; Daux et al., 2000), * Corresponding author.”
The numerical simulation of fatigue crack growth using extended finite element method (2012, methodology): “Till date, XFEMhas extensively used to solve the problems of fracture mechanics including crack growth with frictional contact [17], cohesive crack propagation [18–21], quasi-static crack growth [22], arbitrary branched and intersecting cracks [23], and cracks in shells [24], fatigue crack propagati”
X-FEM explicit dynamics for constant strain elements to alleviate mesh constraints on internal or external boundaries (2008, background): “The linear and bilinear weak forms are simply integrated on the matter part of the elements [8,12].”
Integrated layout design of multi-component systems using XFEM and analytical sensitivity analysis (2012, background): “[31] and Miegroet and Duysinx [29], the inconvenience lies in that this simplification is only suitable to material–void”
Fracture modeling using meshless methods and level sets in 3D: Framework and modeling (2012, background): “and can be used to enrich the approximation around a crack tip [34, 35], where r and are the local polar coordinates of x with respect to the point lying on the crack front and closest to x.”
The MITC3 shell finite element enriched by interpolation covers (2014, methodology): “[8] employed enrichment functions to account for various singularities in solid mechanics problems.”
A cohesive segments method for the simulation of crack growth (2003, neutral): “[29]:”