A local multigrid X-FEM strategy for 3-D crack propagation

A multiscale method for 3‐D crack propagation simulation in large structures is proposed. The method is based on the extended finite element method (X‐FEM). The asymptotic behavior of the crack front is accurately modeled using enriched elements and no remeshing is required during crack propagation....

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Bibliographic Details
Published in:International journal for numerical methods in engineering 2009-01, Vol.77 (4), p.581-600
Main Authors: Rannou, J., Gravouil, A., Baïetto-Dubourg, M. C.
Format: Article
Language:English
Subjects:
3-D crack growth
Computational techniques
Engineering Sciences
Exact sciences and technology
fatigue
Fracture mechanics (crack, fatigue, damage...)
Fundamental areas of phenomenology (including applications)
level sets
Mathematical methods in physics
Mechanics
multigrid
Physics
Solid mechanics
Structural and continuum mechanics
X-FEM
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Summary:A multiscale method for 3‐D crack propagation simulation in large structures is proposed. The method is based on the extended finite element method (X‐FEM). The asymptotic behavior of the crack front is accurately modeled using enriched elements and no remeshing is required during crack propagation. However, the different scales involved in fracture mechanics problems can differ by several orders of magnitude and industrial meshes are usually not designed to account for small cracks. Enrichments are therefore useless if the crack is too small compared with the element size. To overcome this drawback, a project combining different numerical techniques was started. The first step was the implementation of a global multigrid algorithm within the X‐FEM framework and was presented in a previous paper (Eur. J. Comput. Mech. 2007; 16:161–182). This work emphasized the high efficiency in cpu time but highlighted that mesh refinement is required on localized areas only (cracks, inclusions, steep gradient zones). This paper aims at linking the different scales by using a local multigrid approach. The coupling of this technique with the X‐FEM is described and computational aspects dealing with intergrid operators, optimal multiscale enrichment strategy and level sets are pointed out. Examples illustrating the accuracy and efficiency of the method are given. Copyright © 2008 John Wiley & Sons, Ltd.
ISSN:0029-5981
1097-0207
DOI:10.1002/nme.2427