Multiscale homogenization in Kirchhoff's nonlinear plate theory

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 $\ep^2$.