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

Jean-Francois Babadjian·Margarida Baia
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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 $Γ$-convergence analysis, techniques of two-scale convergence and a decoupling procedure between the oscillating variable and the in-plane variable.

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Jean-Francois Babadjian, Margarida Baia. 2006-04-26. 3D-2D analysis of a thin film with periodic microstructure. https://arxiv.org/abs/math/0604566

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