On the derivation of homogenized bending plate model

We derive, via simultaneous homogenization and dimension reduction, the $\mathrm{\Gamma }$-limit for thin elastic plates of thickness $h$ whose energy density oscillates on a scale $\text{eh}$ such that ${\text{eh}}^2\ll h\ll \text{eh}$. We consider the energy scaling that corresponds to Kirchhoff’s nonlinear bending theory of plates.