Bending of thin periodic plates

Mikhail Cherdantsev; Kirill Cherednichenko

doi:10.1007/s00526-015-0932-0

Bending of thin periodic plates

Mikhail Cherdantsev, Kirill Cherednichenko

Cardiff University

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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 language	English
Pages (from-to)	4079-4117
Number of pages	39
Journal	Calculus of Variations and Partial Differential Equations
Volume	54
Issue number	4
Early online date	13 Nov 2015
DOIs	https://doi.org/10.1007/s00526-015-0932-0
Publication status	Published - 1 Dec 2015

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10.1007/s00526-015-0932-0Licence: CC BY

Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory
Cherednichenko, K. (PI)
Engineering and Physical Sciences Research Council
23/07/14 → 22/06/19
Project: Research council

Kirill Cherednichenko
- K.Cherednichenkobath.acuk
Person: Research & Teaching

Cite this

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title = "Bending of thin periodic plates",

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.",

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AU - Cherednichenko, Kirill

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AB - 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.

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DO - 10.1007/s00526-015-0932-0

M3 - Article

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JO - Calculus of Variations and Partial Differential Equations

JF - Calculus of Variations and Partial Differential Equations

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Bending of thin periodic plates

Abstract

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Mathematical Foundations of Metamaterials: Homogenisation, Dissipation and Operator Theory

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Kirill Cherednichenko

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