A new fully coupled two-scales modelling for mechanical problems involving microstructure: The 95/5 technique

Computer Methods in Applied Mechanics and Engineering

Volumn 196, Issue 21-24, 2007, Pages 2325-2337

  Missoum Benziane, D ^a   Ryckelynck, D ^a   Chinesta, F ^a  

^a CNRS   (France)

Author keywords

Computational homogenization; Constrained natural element method; Model reduction; Multi scale problems; Numerical modelling

Indexed keywords

APPROXIMATION THEORY; COMPUTATIONAL METHODS; HOMOGENIZATION METHOD; MATHEMATICAL MODELS;

COMPUTATIONAL HOMOGENIZATION; CONSTRAINED ELEMENT METHOD; MULTI-SCALE PROBLEMS;

COMPUTATIONAL MECHANICS;

APPROXIMATION THEORY; COMPUTATIONAL MECHANICS; COMPUTATIONAL METHODS; HOMOGENIZATION METHOD; MATHEMATICAL MODELS;

EID: 33947613145     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2006.10.013     Document Type: Article

References (22)

1. Alfaro I., Yvonnet J., Cueto E., Doblaré M., and Chinesta F. Meshless methods with application to metal forming. Comput. Methods Appl. Mech. Engrg. 195 48-49 (2006) 6661-6675
2. Ben Dhia H. Problèmes mécaniques multi Echelles: la méthode Arlequin. C.R. ACAD. SCI. I-MATH. 326 (1998) 899-904
3. Chen J.S., Wu C.T., and Yoon Y. A stabilized conforming nodal integration for Galerkin mesh-free methods. Int. J. Numer. Methods Engrg. 50 2 (2001) 435-466
4. Chen J.S., Yoon S., and Wu C.T. Non-linear version of stabilized conforming nodal integration for Galerkin mesh-free methods. Int. J. Numer. Methods Engrg. 53 (2002) 2587-2615
5. Cueto E., Doblaré M., and Gracia L. Imposing essential boundary conditions in the natural element method by means of density-scaled Alpha-shapes. Int. J. Numer. Methods Engrg. 49 (2000) 519-546
6. Dolbow J., and Belytschko T. Numerical integration of the Galerkin weak forme in meshfree methods. Comput. Mech. 23 (1999) 219-230
7. Farhat C., and Roux F.X. A method of finite element tearing and interconnecting and its parallel solution algorithm. Int. J. Numer. Methods Engrg. 32 (1991) 1205-1227
8. Gonzalez D., Cueto E., Martinez M.A., and Doblaré M. Numerical integration in Natural neighbor Galerkin methods. Int. J. Numer. Methods Engrg. 60 (2004) 2077-2104
9. Ladeveze P., Loiseau O., and Dureisseix D. A micro-macro and parallel computational strategy for highly heterogeneous structures. Int. J. Numer. Methods Engrg. 52 (2001) 121-138
10. Ladeveze P., and Pelle J.P. La maitrise du calcul en mécanique linéaire et non-linéaire (2001), Hermès Science Publications, Paris
11. Ladeveze P., and Nouy A. On a multiscale computational strategy with time and space homogenization for structural mechanics. Comput. Methods Appl. Mech. Engrg. 192 (2003) 3061-3087
12. Martinez M.A., Cueto E., Doblaré M., and Chinesta F. A meshless simulation of injection processes involving short fibers composites. Int. J. Forming Process. 4 (2001) 217-236
13. Martinez M.A., Cueto E., Doblaré M., and Chinesta F. Updated lagrangian free surface flow simulations with natural neighbour Galerkin methods. Int. J. Numer. Methods Engrg. 60 (2004) 2105-2129
14. Sambridge M., Braun J., and McQueen M. Geophysical parameterization and interpolation of irregular data using natural neighbors. Geophys. J. Int. 122 (1995) 837-857
15. Sibson R. A vector identity for the Dirichlet tesselations. Math. Proc. Cambridge Philosophical Soc. 87 (1980) 151-155
16. Sukumar N., Moran B., and Belytschko T. The natural elements method in solid mechanics. Int. J. Numer. Methods Engrg. 43 (1998) 839-887
17. Takano N., and Okuno Y. Three-scale finite element analysis of heterogeneous media by asymptotic homogenization and mesh superposition methods. Int. J. Solids Struct. 41 (2004) 4121-4135
18. Traversoni L. Natural neighbor finite elements. International Conference on Hydraulic Engineering Software Hydrosoft Proceedings vol. 2 (1994), Computational Mechanics Publications, England 291-297
19. Yoo J., Moran B., and Chen J.S. Stabilized conforming nodal integration in the natural-element method. Int. J. Numer. Methods Engrg. 60 (1998) 861-890
20. Yvonnet J., Ryckelynck D., Lorong P., and Chinesta F. Interpolation naturelle sur les domaines non-convexes par l'tilisation du diagramme de Voronoi contraint: méthode des eléments c-naturels. Rev. Euro. élément. Finis. 13 (2003) 487-509
21. Yvonnet J., Ryckelynck D., Lorong P., and Chinesta F. A new extension of the natural element method for non-convex and discontinuous domains: the constrained natural element method (C-NEM). Int. J. Numer. Methods Engrg. 60 (2004) 1451-1474
22. Yvonnet J., Chinesta F., Lorong P., and Rynckelynck D. The constrained natural element method (C-NEM) for treating thermal models involving moving interfaces. Int J Thermal Sci. 44 (2005) 559-569