Derivation of a homogenized nonlinear plate theory from 3d elasticity

TL;DR

This paper develops a new nonlinear plate theory by combining homogenization and dimension reduction techniques, capturing the effects of microscopic oscillations in material properties on the macroscopic behavior of thin elastic plates.

Contribution

It introduces a novel derivation of a homogenized nonlinear plate model from 3D elasticity, accounting for oscillating energy densities at different scales.

Findings

Derivation of Gamma-limit for thin plates with oscillating energy density

Unified framework for homogenization and dimension reduction in nonlinear elasticity

Applicable to materials with microstructure scales comparable or smaller than plate thickness

Abstract

We derive, via simultaneous homogenization and dimension reduction, the Gamma-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the film thickness. We consider the energy scaling that corresponds to Kirchhoff's nonlinear bending theory of plates.