This paper addresses the simultaneous homogenization and dimension reduction of thin composite plates reinforced with rigid substructures, within the framework of non-linear elasticity. The reference (undeformed) configuration consists of a periodically perforated elastic matrix, where the holes are occupied by rigid inclusions. We first establish a decomposition of the deformation for such composite structures. Under the assumption that the thickness parameter delta δ is asymptotically smaller than the periodicity epsilon ε, we derive a reduced asymptotic model as both parameters tend to zero. Using rescaled unfolding operators, we characterize the limiting behaviour of the Green–St. Venant strain tensor. Through upper Gamma Γ -convergence, we obtain the homogenized limit energy and establish the existence of a minimizer. The resulting limit model is of constrained Kármán type, where the limiting displacement satisfies a first-order infinitesimal isometry constraint.
Chakrabortty et al. (Wed,) studied this question.