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

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.