Bending of thin periodic plates

Mikhail Cherdantsev, Kirill Cherednichenko

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Abstract

We show that nonlinearly elastic plates of thickness h→0 with an ε -periodic structure such that ε−2h→0 exhibit non-standard behaviour in the asymptotic two-dimensional reduction from three-dimensional elasticity: in general, their effective stored-energy density is “discontinuously anisotropic” in all directions. The proof relies on a new result concerning an additional isometric constraint that deformation fields must satisfy on the microscale.
Original languageEnglish
Pages (from-to)4079-4117
Number of pages39
JournalCalculus of Variations and Partial Differential Equations
Volume54
Issue number4
Early online date13 Nov 2015
DOIs
Publication statusPublished - 1 Dec 2015

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