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Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. Homogenization of Perforated Elastic Structures
 Journal of elasticity 141 (2020), Nr.2, S.181225 ISSN: 03743535 (Print) ISSN: 15732681 (Online) 

 Englisch 
 Zeitschriftenaufsatz, Elektronische Publikation 
 Fraunhofer ITWM () 
Abstract
The paper is dedicated to the asymptotic behavior of εperiodically perforated elastic (3dimensional, platelike or beamlike) structures as ε→0. In case of platelike or beamlike structures the asymptotic reduction of dimension from 3D to 2D or 1D respectively takes place. An example of the structure under consideration can be obtained by a periodic repetition of an elementary “flattened” ball or cylinder for platelike or beamlike structures in such a way that the contact surface between two neighboring balls/cylinders has a nonzero measure. Since the domain occupied by the structure might have a nonLipschitz boundary, the classical homogenization approach based on the extension cannot be used. Therefore, for obtaining Korn’s inequalities, which are used for the derivation of a priori estimates, we use the approach based on interpolation. In case of platelike and beamlike structures the proof of Korn’s inequalities is based on the displacement decomposition for a plate or a beam, respectively. In order to pass to the limit as ε→0 we use the periodic unfolding method.