Multiscale homogenization in Kirchhoff's nonlinear plate theory

TL;DR

This paper investigates how multiscale homogenization interacts with dimension reduction in nonlinear elastic thin plates, deriving different limit models based on the relative scales of thickness and heterogeneity.

Contribution

It introduces a comprehensive analysis of the combined effects of multiscale homogenization and dimension reduction in Kirchhoff's nonlinear plate theory, identifying various limit models.

Findings

Different limit models depending on the ratio of thickness to homogenization scales

Characterization of the interplay between multiscale effects and nonlinear bending

Extension of homogenization techniques to nonlinear plate theories

Abstract

The interplay between multiscale homogenization and dimension reduction for nonlinear elastic thin plates is analyzed in the case in which the scaling of the energy corresponds to Kirchhoff's nonlinear bending theory for plates. Different limit models are deduced depending on the relative ratio between the thickness parameter $h$ and the two homogenization scales $\ep$ and $\ep^2$.