ARTICLE
Nonlinear homogenization of heterogeneous periodic plates of Reissner-Mindlin type
 
 
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University of Lille, Department of Mathematic, Lille, French
CORRESPONDING AUTHOR
Pruchnicki Erick   

Mathematic, University of Lille, France
Online publication date: 2020-04-15
Publication date: 2020-04-15
Submission date: 2019-10-09
Acceptance date: 2019-11-06
 
Journal of Theoretical and Applied Mechanics 2020;58(2):317–323
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ABSTRACT
In this paper, we propose a multiscale finite-strain plate theory for a composite nonlinear plate described by a repetitive periodic heterogeneity. We consider two scales, the macroscopic scale is linked to the entire plate and the microscopic scale is linked to the size of the heterogeneity. At the macroscopic scale, we approximate the displacement field by the Reissner-Mindlin model. By considering the equivalence between variations of the macroscopic elastic energy at each point of the mid surface and the microscopic one, we deduce that the macroscopic stress resultants can be expressed in terms of the microscopic stress.
 
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