Application de la méthode X-FEM à la résolution de problèmes de micromécanique
Keywords:
homogenization, X-FEM, partition of unity, level setAbstract
The eXtended Finite Element Method (X-FEM) allows one to enrich finite element approximation space, thus accounting for discontinuities inside an element. This method is applied in this paper to the solution of micromechanical problem, in order to simplify the mesh generation, since it does not need to conform to the material interfaces. A new enrichment function is proposed, which turns out to have the same accuracy as the classical finite element method. Numerical experiments are presented, for material applications, and for a strandedrope structure.
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References
[BEL 03] BELYTSCHKO T., PARIMI C., MOËS N., SUKUMAR N., USUI S., « Structured extended
finite element methods for solids defined by implicit surfaces », International Journal
for Numerical Methods in Engineering, vol. 56, 2003, p. 609–635.
[BÖH 98] BÖHM H., « A Short Introduction to Basic Aspects of Continuum Micromechanics
», Cdl-fmd report 3-1998, http ://ilfb.tuwien.ac.at/links/mom_m.html, 1998, TUWien,
Vienna.
[DUM 90] DUMONTET H., Homogénéisation et effets de bords dans les matériaux composites,
Thèse d’Etat, Université Paris 6, 1990.
[MEL 96] MELENK J., BABUŠKA I., « The Partition of Unity Finite Element Method : Basic
theory and applications », Comput. Meth. Appl. Mech. Eng., vol. 39, 1996, p. 289-314.
[MIC 99] MICHEL J., MOULINEC H., SUQUET P., « Effective properties of composite materials
with periodic microstruture : a computational approach », Comput. Meth. Appl. Mech.
Eng., vol. 172, no 1-4, 1999, p. 109-143.
[MOË 99] MOËS N., DOLBOW J., BELYTSCHKO T., « A finite element method for crack
growth without remeshing », International Journal for Numerical Methods in Engineering,
vol. 46, 1999, p. 131-150.
[MOË 00] MOËS N., Contributions au calcul des structures : Une extension de la méthode des
éléments finis. Le contrôle des calculs éléments finis non linéaires, Mémoire d’Habilitation,
Ecole Normale Supérieure de Cachan, 2000.
[MOË 03] MOËS N., CLOIREC M., CARTRAUD P., REMACLE J., « A computational approach
to handle complex microstructure geometries », Comput. Meth. Appl. Mech. Eng., vol. 192,
, p. 3163-3177.
[NAW 00] NAWROCKI A., LABROSSE M., « A finite element model for simple straight wire
rope », Computers and Structures, vol. 77, 2000, p. 345-359.
[SET 99] SETHIAN J. A., Level Set Methods & Fast Marching Methods : Evolving Interfaces
in Computational Geometry, Fluid Mechanics, Computer Vision, and Materials Science,
Cambridge University Press, Cambridge, UK, 1999.
[SUK 01] SUKUMAR N., CHOPP D. L., MOËS N., BELYTSCHKO T., « Modeling Holes and
Inclusions by Level Sets in the Extended Finite Element Method », Comp. Meth. in Applied
Mech. and Engrg., vol. 190, 2001, p. 6183–6200.
