Homogenization of perforated elastic structures

The paper is dedicated to the asymptotic behavior of periodically perforated elastic domains (3D, plate-like or beam-like). We homogenize these structures, passing to the limit w.r.t. the period. In case of plate-like or beam-like structures we simultaneously proceed to a dimension reduction. These periodic structures can be made e.g. of balls or cylinders glued, so that the surface in contact has a non-zero measure. Since the boundaries of these structures might be non-Lipschitz, the classical extension approach does not serve. We will proceed using interpolations. The Korn inequalities in the case of thin structures are based on the decomposition of beam or plate displacements. For the asymptotic behavior the unfolding and rescaling operators are used