New crack‐tip elements for XFEM and applications to cohesive cracks

By Goangseup Zi, Ted Belytschko. 2003

625 citations recorded by the source corpus.

Subfields: Mechanical Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/2d47417e20db0b4006bacd5b4e14e476497b4cd5

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In Mechanical Engineering

In Mechanics of Materials

Citations in the corpus

Extended meshfree methods without branch enrichment for cohesive cracks (2007, methodology): “Zi and Belytschko [51] proposed a simple idea to enrich triangular elements with only the sign function (11) without using the the branch enrichment even when the crack tip is located inside of an element, not on the edge.”
A geometrically non-linear three-dimensional cohesive crack method for reinforced concrete structures (2008, positive): “the local partition of unity by Belytschko and his collaborators [18–21] where the crack can propagate arbitrarily in an element without remeshing.”
An extended finite element method with analytical enrichment for cohesive crack modeling (2009, methodology): “For cohesive cracks they modified all of the LEFM functions replacing the √ r factors with r , as Moës and Belytschko [35] had done with the discontinuous term alone.”
Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling (2011, methodology): “In [15], an extrinsic enriched meshless method is developed for 3D fracture modelling where the crack tip is closed by modifying the nodal support, and which is similar to the idea used in the XFEM [16].”
A Meshfree Method based on the Local Partition of Unity for Cohesive Cracks (2007, background): “The easiest way is to control the crack length, [45].”
A contact algorithm for frictional crack propagation with the extended finite element method (2008, methodology): “Following the approach in [24, 39], we show a typical crack tip constant strain triangular (CST) element in Figure 2.”
Extended finite element method in computational fracture mechanics: a retrospective examination (2015, neutral): “The use of a shifted enrichment function (Zi and Belytschko 2003) was introduced in part to facilitate plotting and to avoid the presence of blending elements when certain enrichment functions are used.”
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”
Crack propagation criteria in the framework of X‐FEM‐based structural analyses (2007, neutral): “Two criteria are based on local information from the vicinity of the individual crack tip and two criteria have a global character: a principal stress criterion based on the averaged stresses around the crack tip [14], a maximum circumferential stress criterion based on the stress intensity factors ”