Multi-scale computational homogenization: Trends and challenges

Journal of Computational and Applied Mathematics

Volumn 234, Issue 7, 2010, Pages 2175-2182

  Geers, M G D ^a   Kouznetsova, V G ^a,b   Brekelmans, W A M ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^b MATERIALS INNOVATION INSTITUTE M2I   (Netherlands)

Author keywords

Coarse graining; Homogenization; Multi scale

Indexed keywords

COARSE GRAINING; COMPUTATIONAL HOMOGENIZATION; DOWN-SCALING; MECHANICS OF MATERIALS; MULTISCALES; STRUCTURAL ENGINEERING; UPSCALING;

HOMOGENIZATION METHOD;

EID: 77955306909     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2009.08.077     Document Type: Conference Paper

References (42)

1. E.W. Engquist B, X.T. Li, W. Ren, and E. Vanden-Eijnden Commun. Comput. Phys. 2 3 2007 367 450
2. S. Ahuja, V. Yakhot, and I.G. Kevrekidis Phys. Fluids 20 3 2008 article 035111
3. J. Renard, and M.F. Marmonier Aerosp. Sci. Technol. 1987 37 51
4. P. Suquet A. Sawczuck, G. Bianchi, Plasticity Today: Modelling, Methods and Applications 1985 Elsevier Applied Science Publishers 279 310
5. J.M. Guedes, and N. Kikuchi Comput. Methods Appl. Mech. Engrg. 83 1990 143 198
6. S. Ghosh, K. Lee, and S. Moorthy Internat. J. Solids Structures 32 1995 27 62
7. R.J.M. Smit, W.A.M. Brekelmans, and H.E.H. Meijer Comput. Methods Appl. Mech. Engrg. 155 1998 181 192
8. H. Moulinec, and P. Suquet Comput. Methods Appl. Mech. Engrg. 157 1998 69 94
9. C. Miehe, J. Schrder, and J. Schotte Comput. Methods Appl. Mech. Engrg. 171 1999 387 418
10. C. Miehe, J. Schotte, and J. Schrder Comput. Mat. Sci. 16 1-4 1999 372 382
11. K. Terada, M. Hori, T. Kyoya, and N Kikuchi Internat. J. Solids Structures 37 16 2000 2285 2311
12. F. Feyel, and J.L. Chaboche Comput. Methods Appl. Mech. Engrg. 183 2000 309 330
13. K. Terada, and N. Kikuchi Comput. Methods Appl. Mech. Engrg. 190 4041 2001 5247 5464
14. V.G. Kouznetsova, W.A.M. Brekelmans, and F.P.T. Baaijens Comput. Mech. 27 1 2001 37 48
15. C. Miehe, and A. Koch Arch. Appl. Mech. 72 2002 300 317
16. C. Miehe, and C.G. Bayreuther Internat. J. Numer. Methods Engrg. 71 10 2007 1135 1180
17. C. Miehe Internat. J. Numer. Methods Engrg. 55 2002 1285 1322
18. K. Matsui, K. Terada, and K. Yuge Comput. & Structures 82 7-8 2004 593 606
19. C. McVeigh, F. Vernerey, W.K. Liu, and L.C. Brinson Comput. Methods Appl. Mech. Engrg. 195 3740 2006 5053 5076
20. I. Temizer, and T.I. Zohdi Comput. Mech. 40 2 2007 281 298
21. M. Hain, and P. Wriggers Finite Elem. Anal. Des. 44 5 2008 233 244
22. Z. Yuan, and J. Fish Internat. J. Numer. Methods Engrg. 73 3 2008 361 380
23. M.G.D. Geers, V.G. Kouznetsova, and W.A.M. Brekelmans Jnl. de Phys. IV 11 5 2001 145 152
24. V.G. Kouznetsova, M.G.D. Geers, and W.A.M. Brekelmans Internat. J. Numer. Methods Engrg. 54 2002 1235 1260
25. M.G.D. Geers, V.G. Kouznetsova, and W.A.M. Brekelmans Int. J. Multiscale Comp. Engng. 1 4 2003 371 386
26. V.G. Kouznetsova, M.G.D. Geers, and W.A.M. Brekelmans Int. J. Multiscale Comp. Engng. 2 4 2004 575 598
27. V.G. Kouznetsova, M.G.D. Geers, and W.A.M. Brekelmans Comput. Methods Appl. Mech. Engrg. 193 2004 5525 5550
28. L. Kaczmarczyk, C. Pearce, and N. Bicanic Internat. J. Numer. Methods Engrg. 74 3 2008 506 522
29. T.J. Massart, R.H.J. Peerlings, and M.G.D. Geers Internat. J. Numer. Methods Engrg. 69 5 2007 1022 1059
30. T.J. Massart, R.H.J. Peerlings, and M.G.D. Geers Int. J. Damage Mech. 16 2007 199 226
31. I.M. Gitman, H. Askes, and L.J. Sluys Eur. J. Mech. A Solids 27 3 2008 302 327
32. S. Loehnert, and T. Belytschko Internat. J. Numer. Methods Engrg. 71 12 2007 1466 1482
33. T. Belytschko, S. Loehnert, and J.H. Song Internat. J. Numer. Methods Engrg. 73 6 2008 869 894
34. M.G.D. Geers, E.W.C. Coenen, and V.G. Kouznetsova Mod. Simul. Mat. Sci. Engng. 15 2007 S393 S404
35. B.A. Schrefler, and M. Lefik Struct. Eng. Mech. 4 6 1996 613 630
36. P. Cartraud, and T. Messager Internat. J. Solids Structures 43 34 2006 686 696
37. I. zdemir, W.A.M. Brekelmans, and M.G.D. Geers Internat. J. Numer. Methods Engrg. 73 2 2008 185 204
38. E. Monteiro, J. Yvonnet, and Q.C. He Comput. Mat. Sci. 42 4 2008 704 712
39. H.W. Zhang, S. Zhang, J.Y. Bi, and B.A. Schrefler Internat. J. Numer. Methods Engrg. 69 1 2007 87 113
40. I. zdemir, W.A.M. Brekelmans, and M.G.D. Geers Comput. Methods Appl. Mech. Engrg. 198 34 2008 602 613
41. K. Matous, M.G. Kulkarni, and P.H. Geubelle J. Mech. Phys. Solids 56 4 2008 1511 1533
42. A. Abdulle, and B. Engquist Multiscale Model. Simul. 6 4 2007 1059 1084