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Derivation of a homogenized nonlinear plate theory from 3d elasticity
Peter Hornung, Stefan Neukamm and Igor Velčić
We derive, via simultaneous homogenization and dimension reduction, the $\Gamma$-limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the film thickness. We consider the energy scaling that corresponds to Kirchhoff's nonlinear bending theory of plates.