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

J.-F. Babadjian
L.P.M.T.M.
Université Paris Nord
93430, Villetaneuse, France
jfb@galilee.univ-paris13.fr

and

M. Baía
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
mbaia@andrew.cmu.edu

Abstract. 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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