High-order extended finite element method for cracked domains
Article first published online: 21 JUL 2005
Copyright © 2005 John Wiley & Sons, Ltd.
International Journal for Numerical Methods in Engineering
Volume 64, Issue 3, pages 354–381, 21 September 2005
How to Cite
Laborde, P., Pommier, J., Renard, Y. and Salaün, M. (2005), High-order extended finite element method for cracked domains. Int. J. Numer. Meth. Engng., 64: 354–381. doi: 10.1002/nme.1370
- Issue published online: 18 AUG 2005
- Article first published online: 21 JUL 2005
- Manuscript Accepted: 4 APR 2005
- Manuscript Revised: 28 JAN 2005
- Manuscript Received: 15 OCT 2004
- finite elements;
- extended finite element method;
- rate of convergence
The aim of the paper is to study the capabilities of the extended finite element method (XFEM) to achieve accurate computations in non-smooth situations such as crack problems. Although the XFEM method ensures a weaker error than classical finite element methods, the rate of convergence is not improved when the mesh parameter h is going to zero because of the presence of a singularity. The difficulty can be overcome by modifying the enrichment of the finite element basis with the asymptotic crack tip displacement solutions as well as with the Heaviside function. Numerical simulations show that the modified XFEM method achieves an optimal rate of convergence (i.e. like in a standard finite element method for a smooth problem). Copyright © 2005 John Wiley & Sons, Ltd.