Bending of thin periodic plates

Cherdantsev, Mikhail ORCID: https://orcid.org/0000-0002-5175-5767 and Cherednichenko, Kirill 2015. Bending of thin periodic plates. Calculus of Variations and Partial Differential Equations 54 , pp. 4079-4117. 10.1007/s00526-015-0932-0

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Abstract

We show that nonlinearly elastic plates of thickness h → 0 with an ε-periodic structure such that ε^2 h → 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.

Item Type:	Article
Date Type:	Publication
Status:	Published
Schools:	Mathematics
Subjects:	Q Science > QA Mathematics
Additional Information:	This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Publisher:	Springer Verlag
ISSN:	0944-2669
Funders:	EPSRC
Date of First Compliant Deposit:	30 March 2016
Date of Acceptance:	14 September 2015
Last Modified:	06 May 2023 05:06
URI:	https://orca.cardiff.ac.uk/id/eprint/81785

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