3D-2D asymptotic analysis for Inhomogeneous thin films

Abstract

A dimension reduction analysis is undertaken using Γ-convergence techniques within a relaxation theory for 3D nonlinear elastic thin domains of the form Ωε := {(X1,X2,X3) : (X1,X2) ∈ ω, |X3| < εfε(X1,X2)}, where ω is a bounded domain of ℝ2 and fε is an ε-dependent profile. An abstract representation of the effective 2D energy is obtained, and specific characterizations are found for nonhomogeneous plate models, periodic profiles, and within the context of optimal design for thin films.