Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling
By Xiaoying Zhuang, Charles E. Augarde, Stéphane P.A. Bordas. 2011
124 citations recorded by the source corpus.
Fracture modelling using numerical methods is well‐advanced in 2D using techniques such as the extended finite element method (XFEM). The use of meshless methods for these problems lags somewhat behind, but the potential benefits of no meshing (particularly in 3D) prompt continued research into their development. In methods where the crack face is not explicitly modelled (as the edge of an element for instance), two procedures are instead used to associate the displacement jump with the crack surface: the visibility criterion and the diffraction method. The visibility criterion is simple to implement and efficient to compute, especially with the help of level set coordinates. However, spurious discontinuities have been reported around crack tips using the visibility criterion, whereas implementing the diffraction method in 3D is much more complicated than the visibility criterion. In this paper, a tying procedure is proposed to remove the difficulty with the visibility criterion so that crack tip closure can be ensured while the advantages of the visibility criterion can be preserved. The formulation is based on the use of level set coordinates and the element‐free Galerkin method, and is generally applicable for single or multiple crack problems in 2D or 3D. The paper explains the formulation and provides verification of the method against a number of 2D crack problems. Copyright © 2011 John Wiley & Sons, Ltd.
Subfields: Civil and Structural Engineering, Mechanics of Materials
View Paper: https://www.semanticscholar.org/paper/1888f087030f1d2dff94e33d9e33f43fde5ad403
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Civil and Structural Engineering
- Hong Zheng
- Xiaoying Zhuang
- Yongchang Cai
- Miguel Cervera
- Michele Chiumenti
- G. Barbat
- Charles E. Augarde
- Feng Liu
In Mechanics of Materials
- Hong Zheng
- Xiaoying Zhuang
- Miguel Cervera
- Michele Chiumenti
- Charles E. Augarde
- Yongchang Cai
- G. Barbat
- Yongtao Yang
Citations in the corpus
- The MLS-based numerical manifold method with applications to crack analysis (2014, background): “Recently, Barbieri et al. (2012), Zhuang et al. (2011) and some others designed new treatments to solve the above issues successfully.”
- Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy (2017, methodology): “Models developed with this approach include, but are not limited to, cohesive interface elements with or without remeshing [15-22], elements with embedded strong discontinuities [23-28], extended finite elements methods [29-34], and meshless and particle methods [35-39].”
- A new weight‐function enrichment in meshless methods for multiple cracks in linear elasticity (2012, background): “Very recently, [40] dealt with this issue, proposing a tying procedure to remove the spurious crack extension generated by the visibility criterion.”
- A meshless sub-region radial point interpolation method for accurate calculation of crack tip fields (2014, methodology): “As has been in shown [25] the number of integration points required for results of acceptable accuracy is typically about 10 times the total number of nodes, and is heighten for fracture modelling in 2D to 11~12 times for single crack problem in 2D [19].”
- Meshfree Methods: Progress Made after 20 Years (2017, unknown): “Alterna-tively, level-set methods for tracking of complicated crack geometry have been proposed (Bordas et al. 2008; Ventura et al. 2002; Zhuang et al. 2011).”