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

Published online by Cambridge University Press:  12 July 2007

Jean-François Babadjian  and
Margarida Baía
Jean-François Babadjian
Affiliation:
Laboratoire des Propriétés Mécaniques et Thermodynamiques des Matériaux (LPMTM), Université Paris Nord, 93430 Villetaneuse, France (jfb@galilee.univ-paris13.fr)
Margarida Baía
Affiliation:
Department of Mathematical Science, Carnegie Mellon University, Pittsburgh, PA 15213, USA (mbaia@andrew.cmu.edu)
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Abstract

In this article we study the behaviour 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 three-dimensional–two-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.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 136 , Issue 2 , April 2006 , pp. 223 - 243
Copyright
Copyright © Royal Society of Edinburgh 2006

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