Details
| Original language | English |
|---|---|
| Pages (from-to) | 249-268 |
| Number of pages | 20 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 86 |
| Issue number | 2 |
| Publication status | Published - 21 Jan 2011 |
| Externally published | Yes |
Abstract
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.
Keywords
- Crack tip closure, EFG, Fracture, Level sets, Meshless, Tying procedure, Visibility criterion
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Engineering(all)
- General Engineering
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Engineering, Vol. 86, No. 2, 21.01.2011, p. 249-268.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Accurate fracture modelling using meshless methods, the visibility criterion and level sets
T2 - Formulation and 2D modelling
AU - Zhuang, Xiaoying
AU - Augarde, Charles
AU - Bordas, Stéphane
PY - 2011/1/21
Y1 - 2011/1/21
N2 - 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.
AB - 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.
KW - Crack tip closure
KW - EFG
KW - Fracture
KW - Level sets
KW - Meshless
KW - Tying procedure
KW - Visibility criterion
UR - http://www.scopus.com/inward/record.url?scp=79952695805&partnerID=8YFLogxK
U2 - 10.1002/nme.3063
DO - 10.1002/nme.3063
M3 - Article
AN - SCOPUS:79952695805
VL - 86
SP - 249
EP - 268
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 2
ER -