Free Access
Issue
Math. Model. Nat. Phenom.
Volume 4, Number 1, 2009
Modelling and numerical methods in contact mechanics
Page(s) 88 - 105
DOI https://doi.org/10.1051/mmnp/20094104
Published online 27 January 2009
  1. R.A. Adams. Sobolev Spaces. Academic Press, 1975. [Google Scholar]
  2. E. Béchet, H. Minnebo, N. Moës, B. Burgardt. Improved implementation and robustness study of the x-fem for stress analysis around cracks. Int. J. Numer. Meth. Engng., 64 (2005), 1033–1056. [CrossRef] [Google Scholar]
  3. T. Belytschko, N. Moës, S. Usui, C. Parimi. Arbitrary discontinuities in finite elements. Int. J. Numer. Meth. Engng., 50 (2001), 993–1013. [CrossRef] [Google Scholar]
  4. E. Chahine. Etude mathématique et numérique de méthodes d'éléments finis étendues pour le calcul en domaines fissurés. Thèse de Doctorat de l'INSA de Toulouse, 2008. [Google Scholar]
  5. E. Chahine, P. Laborde, Y. Renard. Crack-tip enrichment in the Xfem method using a cut-off function. To appear in Int. J. Numer. Meth. Engng. [Google Scholar]
  6. E. Chahine, P. Laborde, Y. Renard. Spider Xfem: an extended finite element variant for partially unknown crack-tip displacement. To appear in Europ. J. of Comp. Mech. [Google Scholar]
  7. E. Chahine, P. Laborde, Y. Renard. The extended finite element method with an integral matching condition. Submitted. [Google Scholar]
  8. P.G. Ciarlet. The finite element method for elliptic problems. Studies in Mathematics and its Applications No 4, North Holland, 1978. [Google Scholar]
  9. H. Ben Dhia. Multiscale mechanical problems : the Arlequin method. C. R. Acad. Sci., série I, Paris, 326 (1998), 899–904. [Google Scholar]
  10. M. Dupeux. Mesure des énergies de rupture interfaciale: problématique et exemples de résultats d'essais de gonflement-d'écollement. Mécanique et industrie, 5 (2004), 441–450. [CrossRef] [EDP Sciences] [Google Scholar]
  11. A. Ern, J.-L. Guermond. Éléments finis: théorie, applications, mise en œuvre. Mathématiques et Applications 36, SMAI, Springer-Verlag, 2002. [Google Scholar]
  12. R. Glowinski, J. He, J. Rappaz, J. Wagner. Approximation of multi-scale elliptic problems using patches of elements. C. R. Math. Acad. Sci., Paris, 337 (2003), 679–684. [Google Scholar]
  13. P. Grisvard. Problèmes aux limites dans les polygones - mode d'emploi. EDF Bull. Dirctions Etudes Rech. Sér. C. Math. Inform. 1, MR 87g:35073 (1986), 21–59. [Google Scholar]
  14. P. Grisvard. Singularities in boundary value problems. Masson, 1992. [Google Scholar]
  15. D.B.P. Huynh, A.T. Patera. Reduced basis approximation and a posteriori error estimation for stress intensity factors. Int. J. Numer. Meth. Engng. 72 (2007), 1219–1259. [Google Scholar]
  16. P. Laborde, Y. Renard, J. Pommier, M. Salaün. High order extended finite element method for cracked domains. Int. J. Numer. Meth. Engng., 64 (2005), 354–381. [CrossRef] [Google Scholar]
  17. J. Lemaitre, J.-L. Chaboche. Mechanics of Solid Materials. Cambridge University Press, 1994. [Google Scholar]
  18. J.L. Lions, E. Magenes. Problèmes aux limites non homogènes et applications, volume 1. Dunod, 1968. [Google Scholar]
  19. Y. Maday, E.M. Rønquist. A reduced-basis element method. J. Sci. Comput., 17 (2002), (1-4), 447–459. [Google Scholar]
  20. J.M. Melenk, I. Babuška. The partition of unity finite element method: Basic theory and applications. Comput. Meths. Appl. Mech. Engrg., 139 (1996), 289–314. [CrossRef] [MathSciNet] [Google Scholar]
  21. N. Moës, T. Belytschko. X-fem: Nouvelles frontières pour les éléments finis. Revue européenne des éléments finis, 11 (1999), 131–150. [Google Scholar]
  22. N. Moës, J. Dolbow, T. Belytschko. A finite element method for crack growth without remeshing. Int. J. Numer. Meth. Engng., 46 (1999), 131–150. [CrossRef] [Google Scholar]
  23. A.K. Noor, J.M. Peters. Reduced basis technique for nonlinear analysis of structures. AIAA Journal, 18 (2002), No. 4, 455–462. [CrossRef] [Google Scholar]
  24. Y. Renard, J. Pommier. Getfem++. An open source generic C++ library for finite element methods, http://home.gna.org/getfem. [Google Scholar]
  25. G. Strang, G. Fix. An Analysis of the finite element method. Prentice-Hall, Englewood Cliffs, 1973. [Google Scholar]
  26. T. Strouboulis, I. Babuska, K. Copps. The design and analysis of the generalized finite element method. Comput. Meths. Appl. Mech. Engrg., 181 (2000), 43–69. [CrossRef] [Google Scholar]
  27. T. Strouboulis, I. Babuska, K. Copps. The generalized finite element method: an example of its implementation and illustration of its performance. Int. J. Numer. Meth. Engng., 47 (2000), 1401–1417. [CrossRef] [Google Scholar]
  28. N. Sukumar, Z. Y. Huang, J.-H. Prévost, Z. Suo. Partition of unity enrichment for bimaterial interface cracks. Int. J. Numer. Meth. Engng., 59 (2004), 1075–1102. [CrossRef] [Google Scholar]

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