The interplay between multiscale homogenization and dimension reduction for nonlinear elastic thin plates is analyzed in the case in which the scaling of the energy corresponds to Kirchhoff's nonlinear bending theory for plates. Different limit models are deduced depending on the relative ratio between the thickness parameter h and the two homogenization scales ε and ε 2 .
Abstract. In this paper the notion of two-scale convergence introduced by G. Nguetseng and G. Allaire is extended to the case of bounded sequences in L 1 (Ω), where Ω is any open subset of R N . Three different approaches will be considered: an adaptation of the method used in L p (Ω) with p > 1, a measure-theoretic argument, and the periodic unfolding technique.
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