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On the general homogenization and $\Gamma$-closure for the equations of von Kármán plate from $3D$ nonlinear elasticity
Starting from $3D$ elasticity equations we derive the model of the homogenized von K\'arm\'an plate by means of $\Gamma$-convergence. This generalizes the recent results, where the material oscillations were assumed to be periodic. We also prove the locality of $\Gamma$-closure i.e. that every energy density obtained in this way by mixing $n$ different materials is at almost every point of domain limit of some sequence of the energy densities obtained by periodic homogenization.