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This paper focuses on the simultaneous homogenization and dimension reductionof periodic composite plates within the framework of non-linear elasticity. Thecomposite plate in its reference (undeformed) configuration consists of aperiodic perforated plate made of stiff material with holes filled by softmatrix material. The structure is clamped on a cylindrical part. Two cases ofasymptotic analysis are considered: one without pre-strain and the other withmatrix pre-strain. In both cases, the total elastic energy is in thevon-K\'arm\'an (vK) regime ($\varepsilon^5$).  A new splitting of the displacements is introduced to analyze the asymptoticbehavior. The displacements are decomposed using the Kirchhoff-Love (KL) platedisplacement decomposition. The use of a re-scaling unfolding operator allowsfor deriving the asymptotic behavior of the Green St. Venant's strain tensor interms of displacements. The limit homogenized energy is shown to be of vK typewith linear elastic cell problems, established using the $\Gamma$-convergence.  Additionally, it is shown that for isotropic homogenized material, our limitvK plate is orthotropic. The derived results have practical applications in thedesign and analysis of composite structures.

Dimension reduction and homogenization of composite plate with matrix pre-strain