Geodesic
Homogenization for elasticity problems on periodic networks
Sbornik. Mathematics, Tome 194 (2003) no. 5, pp. 697-732

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It is a noticeable feature of elasticity problems on periodic structures depending on two geometric parameters that their homogenization has a non-classical nature. The most complicated kind of this non-classical homogenization occurs on structures of so-called critical thickness. Homogenization for periodic networks of this type is presented in the paper. 
@article{SM_2003_194_5_a2,
     author = {V. V. Zhikov and S. E. Pastukhova},
     title = {Homogenization for  elasticity problems on periodic networks},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2003_194_5_a2/}
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V. V. Zhikov; S. E. Pastukhova. Homogenization for  elasticity problems on periodic networks. Sbornik. Mathematics, Tome 194 (2003) no. 5, pp. 697-732. http://geodesic.mathdoc.fr/item/SM_2003_194_5_a2/