Application of Multi-Scale Modelling to Some Elastic, Piezoelectric and Electromagnetic Composites

REFERENCES

• Allaire , G. 1992 . “Homogenization and two-scale convergence” . SIAM J. Math. Anal. , 23 ( 6 ) : 1482 – 1518 . [CSA]
   Web of Science ®Google Scholar
• Arbogast , T. , Douglas , J. Jr. and Hornung , U. 1990 . “Derivation of the double porosity model of single phase flow via homogenization theory” . SIAM J. Math. Anal. , 21 : 823 – 836 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Anselme , K. 2000 . “Osteoblast adhesion on biomaterials (Review)” . Biomaterial , 21 : 667 – 681 . [CROSSREF] [CSA]
   PubMed Web of Science ®Google Scholar
• Ávila , A. , Griso , G. and Miara , B. 2005 . “Bandes phononiques interdites en ElasticitE linEarisEe” . C. R. Acad. Sci. Paris, Ser. I , 340 : 933 – 938 . [CSA]
   Google Scholar
• Baiotto , S. and Zidi , M. 2004 . “Theoretical and numerical study of bone remodelling model: The effect of osteocyte cells distribution” . Biomechamics and Modeling in Mechanobiology , 3 ( 1 ) : 6 – 16 . [CROSSREF] [CSA]
   PubMed Web of Science ®Google Scholar
• Bossavit , A. 1995 . Chiral materials by mixing simple ones , ISEM Cardiff .
   Google Scholar
• Bossavit , A. , Griso , G. and Miara , B. 2005 . “Modelling of periodic electromagnetic structures. Bianisotropic materials with memory effects” . J. Math. Pures Appl. , 84 : 819 – 850 . [CSA]
   Google Scholar
• Bouchitte , G. and Felbacq , D. 2004 . “Homogenization near resonances and artificial magnetism from dielectrics” . C. R. Acad. Sci. Paris, Ser. I , 339 : 377 – 382 . [CSA]
   Web of Science ®Google Scholar
• Castillero , Otero and Ramos , Bourgeat . 1998 . “Asymptotic homogenization of laminated piezocomposite material” . Int. J. Solids Structures , 35 ( 5–6 ) : 527 – 541 . [CROSSREF] [CSA]
   Google Scholar
• Cioranescu , A. , Damlamian , A. and Griso , G. 2002 . “Periodic unfolding and homogenization.” . C. R. Acad. Sci. Paris, Ser. I , 335 : 99 – 104 . [CSA]
   Web of Science ®Google Scholar
• Griso , G. and Miara , B. “Photonic band gaps” in preparation
   Google Scholar
• Ghergu , M. , Griso , G. , Labat , B. , Mechkour , H. , Miara , B. , Rohan , E. and Zidi , M. 2006 . “Homogénéisation et piEzoElectricitE. Aide a la conception d'un bio-matEriau, Annals of the University of Craiova” . Math. Comp. Sci. Ser. , 30 ( 1 ) to appear[CSA]
   Google Scholar
• Griso , G. and Miara , B. Periodically Perforated Piezoelectric Structures . Conference SMART'03 . September 2–5 , Jadwisin, Poland.
   Google Scholar
• Miara , B. , Rohan , E. , Zidi , M. and Labat , B. 2005 . “Piezomaterials for bone regeneration design—Homogenization approach” . Journal of Mechanics and Physics of Solids , 53/11 : 2529 – 2556 . [CROSSREF] [CSA]
   Google Scholar
• Miara , B. , Rohan , E. , Zidi , M. and Labat , B. 2004 . Homogenization theory applied to the design of bone bio-material . First European Conference on Micro and Nano technologies . Octobre 2004 , Paris.
   Google Scholar
• Nguetseng , G. 1989 . “A general convergence result for a functioanl related to the theory of homogenization” . SIAM J. Math. Anal. , 20 ( 3 ) : 608 – 623 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Ouchetto , O. , Zouhdi , S. , Bossavit , A. , Griso , G. , Miara , B. and Razek , A. 2005 . “Homogenization of Structured Electromagnetic Materials and metamaterials” . submitted to Journal of Materials Processing Technology , [CSA]
   Google Scholar
• Ouchetto , O. , Zouhdi , S. , Bossavit , A. , Griso , G. , Miara , B. and Razek , A. 2005 . A new approach for the homogenization of three-dimensional metallodielectric lattices: the periodic unfolding method . PECS-VI, International Symposium on Photonic and Electromagnetic Crystal Structures . June 19–24 2005 , Aghia Pelaghia, Crete, Greece.
   Google Scholar
• Pendry , J. B. 1993 . J. Mod. Optics , 41 : 209 [CSA]
   Google Scholar
• Rohan , E. and Miara , B. Microstructural sensitivity of acoustic band gaps . 17th IMACS World Congress . July 11–15 , Paris.
   Google Scholar
• Rohan , E. and Miara , B. On sensitivity of piezoelectric coupling in perforated media with respect to geometry of the microstructure . ECCOMAS Thematic Conference on Smart Structures and Materials . July 18–21 , Lisbon.
   Google Scholar
• Sikavitsas , V. I. , Temeno , J. S. and Mikos , G. A. 2001 . “Biomaterials and bone mechanotransduction (Review)” . Biomaterial , 22 : 2581 – 2593 . [CROSSREF] [CSA]
   PubMed Web of Science ®Google Scholar
• Sigmund , O. and Jensen , J. S. 2003 . “Systematic design of phononic band-gap materials and structures by topology optimization” . Phil. Trans. R. Soc. London A , 361 : 1001 – 1019 . [CROSSREF] [CSA]
   PubMed Web of Science ®Google Scholar
• Silva , C. C. , Thomazini , D. , Pinheiro , A. G. , Aranha , N. , Figueiro , S. D. , Góes , J. C. and Sombra , A. S. B. 2001 . “Collagen-hydroxyapatite films: piezoelectric properties” . Materials Science and Engineering , B86 : 210 – 218 . [CSA]
   Google Scholar
• Telega , J. J. 1991 . “ Piezoelectricity and homogenization. Application to biomechanics ” . In Continuum Models and Discrete Systems , Vol. 2 , 220 – 229 . London : Longman .
   Google Scholar
• Vasseur , J. , Deymier , P. , Frantziskonis , G. , Hong , G. , Djafari-Rouhani , B. and Dobrzynski , L. 1998 . “Experimental evidence for the existence of absolute acoustic band gaps in two-dimensional periodic composite media” . J. Phy. Condens. Matter , 10 : 6051 – 6064 . [CROSSREF] [CSA]
   Web of Science ®Google Scholar
• Wellander , N. 2001 . “Homogenization of the Maxwell equations: Case I. Linear theory” . Applications of Mathematics , 1 : 29 – 51 . [CROSSREF] [CSA]
   Google Scholar
• Yablanovitch , E. 1993 . J. Phys. Condens. Matter , 5 : 2443 [CROSSREF] [CSA]
   Google Scholar