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Crack tip enrichment in the XFEM using a cutoff function |
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| Authors: | Elie Chahine Patrick Laborde Yves Renard |
| Affiliation: | 1. Institut de Mathématiques, UMR CNRS 5215, GMM INSA Toulouse, Complexe Scientifique de Rangueil, 31077 Toulouse Cedex 4, France;2. Institut de Mathématiques, UMR CNRS 5215, UPS Toulouse 3, 118 Route de Narbonne, 31062 Toulouse Cedex 4, France;3. Institut Camille Jordan, CNRS UMR 5208, INSA de Lyon, Université de Lyon, 20 rue Albert Einstein, 69621 Villeurbanne Cedex, France |
| Abstract: | We consider a variant of the eXtended Finite Element Method (XFEM) in which a cutoff function is used to localize the singular enrichment surface. The goal of this variant is to obtain numerically an optimal convergence rate while reducing the computational cost of the classical XFEM with a fixed enrichment area. We give a mathematical result of quasi‐optimal error estimate. One of the key points of this paper is to prove the optimality of the coupling between the singular and the discontinuous enrichments. Finally, we present some numerical computations validating the theoretical result. These computations are compared with those of the classical XFEM and a non‐enriched method. Copyright © 2008 John Wiley & Sons, Ltd. |
| Keywords: | fracture mechanics extended finite element method cutoff function error estimates numerical convergence rate |