Dimension reduction problems for non simple grade two materials

Dimension reduction is used to derive the energy of nonsimple materials graded two thin structures, namely thin films and thin multidomains whose bulk energies have an explicit dependence on the second order derivatives of the displacement. Relaxation and $Gamma$-convergence techniques lead to limit models whic recover Cosserat theory. In details the 3D-2D reduction is studied both in the framwork of Sobolev spaces and in a suitable space of Young measures. The limit model in them ultidomain context provides also explicit junction conditions which involve the Cosserat directors.