3D-2D analysis of a thin film with periodic microstructure

Details 3D-2D analysis of a thin film with periodic microstructure 3D-2D analysis of a thin film with periodic microstructure

2006-04-26

arxiv.org/abs/math/0604566v1

Proc. Roy. Soc. Ed. Sect. A, 136 (2006) 223-243

Mathematics

Analysis of PDEs

19 pages

Scientific paper

The purpose of this article is to study the behavior of a heterogeneous thin film whose microstructure oscillates on a scale that is comparable to that of the thickness of the domain. The argument is based on a 3D-2D dimensional reduction through a $\Gamma$-convergence analysis, techniques of two-scale convergence and a decoupling procedure between the oscillating variable and the in-plane variable.

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