Geodesic
Multiscale modeling of elastic composite materials
Matematičeskoe modelirovanie, Tome 24 (2012) no. 5, pp. 3-20.

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A new homogenization method for periodical multiscale hierarchical structures is proposed. The method allows to obtain effective elastic properties of composite materials with multiscale hierarchical inner structure. Recurrent consequences of local and averaged elastic problems for series of periodicity cells are formulated. Multiscale finite element analysis for local problems was carried out. Computed results of multiscale analysis for the two-scale model of textile composite material are presented.
Keywords: multiscale homogenization method, finite element analysis, effective elastic properties of composite materials. 
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Yu. I. Dimitrienko; A. P. Sokolov. Multiscale modeling of elastic composite materials. Matematičeskoe modelirovanie, Tome 24 (2012) no. 5, pp. 3-20. http://geodesic.mathdoc.fr/item/MM_2012_24_5_a0/

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