Extended finite element method for cohesive crack growth

By Nicolas Moës, Ted Belytschko. 2002

1,595 citations recorded by the source corpus.

The extended finite element method allows one to model displacement discontinuities which do not conform to interelement surfaces. This method is applied to modeling growth of arbitrary cohesive cracks. The growth of the cohesive zone is governed by requiring the stress intensity factors at the tip of the cohesive zone to vanish. This energetic approach avoids the evaluation of stresses at the mathematical tip of the crack. The effectiveness of the proposed approach is demonstrated by simulations of cohesive crack growth in concrete.

Subfields: Building and Construction, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/ddc6ec0f7706fb26e9b0895c87c0943fe8bcbc0f

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In Building and Construction

In Mechanics of Materials

Citations in the corpus

Towards the algorithmic treatment of 3D strong discontinuities (2006, background): “In combination with the extended finite element method, it has been applied e.g. by Wells et al. [13, 15], Möes & Belytschko [14] and Gasser & Holzapfel [17].”
Phase-field modeling of fluid-driven dynamic cracking in porous media (2019, methodology): “Typical discrete approaches exploit remeshing techniques as in [5–8], extended finite element method (XFEM) [9, 10], phantom-node method [11–13], cohesive element method [14, 15] or element-erosion method [16, 17].”
Cohesive models for damage evolution in laminated composites (2005, methodology): “Such elements have recently been developed to create a new modeling strategy known as the XFEM and offer an attractive method for generalized laminate damage analysis (Strouboulis et al., 2001; Moës and Belytschko, 2002; Wells et al., 2002; De Borst, 2003; Remmers 2003; Zi and Belytschko, 2003).”
Thermo-hydro-mechanical modeling of impermeable discontinuity in saturated porous media with X-FEM technique (2012, methodology): “The X-FEM was originally applied in mesh-independent crack propagation problems, including: the crack growth with frictional contact [33], cohesive crack propagation [34–36], stationary and growing cracks [37] and three-dimensional crack propagation [38].”
Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation (2003, methodology): “The X-FEM has been successfully applied to 2-dimensional static and quasi-static crack growth problems (Mo€es et al., 1999; Dolbow, 1999; Dolbow et al., 2000a,b; Dolbow et al., 2001; Mo€es and Belytschko, 2002), with its extension to modeling holes, and branched and intersecting cracks proposed in D”
A high‐order generalized FEM for through‐the‐thickness branched cracks (2007, neutral): “Further, cohesive or frictional contact laws [21, 40–52] can be incorporated by appropriate modifications of the formulation reported in [6, Sec.”
Stress analysis around crack tips in finite strain problems using the eXtended finite element method (2005, methodology): “Several fracture mechanics applications have been solved with the X-FEM approach: crack growth with friction [6], arbitrary branched and intersecting cracks [7], three dimensional crack propagation [8, 9] and cohesive crack simulation [10, 11].”
Derivative recovery and a posteriori error estimate for extended finite elements (2007, background): “For problems with discontinuities in the primal dependent variable (cracks [29, 28, 13], fluid-structure interaction [26]), discontinuous functions are added.”
The extended/generalized finite element method: An overview of the method and its applications (2010, background): “Moës and Belytschko [124] suggest the following cracktip enrichment function ψtip = r k sin θ 2 , (33) with k being either 1, 1.5, or 2.”