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ARTICLE
Nonlinear homogenization of heterogeneous periodic plates of Reissner-Mindlin type
1
University of Lille, Department of Mathematic, Lille, French
Submission date: 2019-10-09
Acceptance date: 2019-11-06
Online publication date: 2020-04-15
Publication date: 2020-04-15
Journal of Theoretical and Applied Mechanics 2020;58(2):317-323
KEYWORDS
TOPICS
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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