Senior Lecturer in Civil Engineering.
Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling
Article first published online: 21 JAN 2011
Copyright © 2011 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
Volume 86, Issue 2, pages 249–268, 15 April 2011
How to Cite
Zhuang, X., Augarde, C. and Bordas, S. (2011), Accurate fracture modelling using meshless methods, the visibility criterion and level sets: Formulation and 2D modelling. Int. J. Numer. Meth. Engng., 86: 249–268. doi: 10.1002/nme.3063
- Issue published online: 14 MAR 2011
- Article first published online: 21 JAN 2011
- Manuscript Accepted: 1 SEP 2010
- Manuscript Revised: 31 AUG 2010
- Manuscript Received: 23 JUN 2010
- level sets;
- crack tip closure;
- visibility criterion;
- tying procedure;
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.