Asymptotic analysis of thin composites under linear and nonlinear elasticity

Thin composite structures with heterogeneous microgeometry arise in many modern engineering applications, including lightweight materials, smart structures, and high-contrast mechanical systems. Their effective behavior depends simultaneously on geometry, material contrast, and scale interactions which makes rigorous reduced modeling mathematically challenging. This thesis develops a variational framework for the asymptotic analysis of thin composite plates in linear and nonlinear elasticity. It studies homogenization, dimension reduction, and, in certain regimes, linearization, with emphasis on periodically perforated plates, matrix pre-strain, and rigid inclusions. Using Gamma-convergence, decomposition techniques, and rescaled unfolding operators, the work derives effective plate models and characterizes the corresponding limit energies.