Plate models in nonlinear elasticity obtained by the process of simultaneous homogenization and dimensional reduction

In the talk we shall discuss about plate models for different regimes obtained by the process of simultaneous homogenization and dimensional reduction with the special emphasis on the von Kármán case. Since we have two small parameters, namely the thickness of the plate $h$ and the oscillations of material $\varepsilon(h)$, the obtained models depend on the relation between these two parameters. We shall discuss the case when they are on the same scale i.e. $\lim_{h \to 0} \frac{h}{\varepsilon(h)}=\gamma \in \langle 0, \infty \rangle$. During the talk we shall also present three new models obtained by this procedure: homogenized von Kármán plate model, periodically wrinkled von Kármán plate and homogenized von Kármán shell model.