A meshless method with enriched weight functions for fatigue crack growth

By Marc Duflot, H. Nguyen‐Dang. 2004

156 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/84fccbdcd58b91b2b1b1636e1f7a185c5a2075ac

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In Civil and Structural Engineering

In Mechanics of Materials

Citations in the corpus

Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling (2011, methodology): “Alternatives are to use improved weight functions [33] and enriched weight functions [34, 35], both of which introduce no additional unknowns.”
A study of the representation of cracks with level sets (2007, background): “In References [12–14], an enrichment by means of special weight functions is proposed.”
A new weight‐function enrichment in meshless methods for multiple cracks in linear elasticity (2012, methodology): “This paper is directly inspired by this idea of modified weight function, which was first proposed by Duflot and coworkers in [28, 29], and [30] although a completely different enriched weight function is proposed.”
XLME interpolants, a seamless bridge between XFEM and enriched meshless methods (2014, methodology): “Also in some enriched meshless methods, no representation of the crack’s topology is needed as this is handled through cracking particles as in [20] or weight-function enrichments as in [21, 22].”
The numerical simulation of fatigue crack growth using extended finite element method (2012, methodology): “For stable crack propagation, the generalized Paris’ law [6] is described as da dN 1⁄4 CðDKIeqÞ ð25Þ”
Meshless methods: A review and computer implementation aspects (2008, background): “[44] suggested an alternative intrinsic enrichment by enriched kernel functions: wc(X) = α√r cos θ 2 w4(X) √ ( θ) U”
Fracture modeling using meshless methods and level sets in 3D: Framework and modeling (2012, methodology): “In [36], a high-order 8 8 integration scheme in square cells is used but is expensive.”
A partition of unity enriched dual boundary element method for accurate computations in fracture mechanics (2011, background): “Such a basis has been considered in finite element context by Benzley [25] and in a meshfree context by Duflot & Nguyen-Dang [26] and Fleming et al.”
A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields (2014, methodology): “Recently, much effort has been directed towards the application of meshless methods to crack problems to overcome the difficulties in traditional numerical methods [9-19].”