Tarnai, T., Fowler, P.W. orcid.org/0000-0003-2106-1104, Guest, S.D. et al. (1 more author) (2022) Equiauxetic hinged Archimedean tilings. Symmetry, 14 (2). 232. ISSN 2073-8994
Abstract
There is increasing interest in two-dimensional and quasi-two-dimensional materials and metamaterials for applications in chemistry, physics and engineering. Some of these applications are driven by the possible auxetic properties of such materials. Auxetic frameworks expand along one direction when subjected to a perpendicular stretching force. An equiauxetic framework has a unique mechanism of expansion (an equiauxetic mode) where the symmetry forces a Poisson’s ratio of −1. Hinged tilings offer opportunities for the design of auxetic and equiauxetic frameworks in 2D, and generic auxetic behaviour can often be detected using a symmetry extension of the scalar counting rule for mobility of periodic body-bar systems. Hinged frameworks based on Archimedean tilings of the plane are considered here. It is known that the regular hexagonal tiling, {63}, leads to an equiauxetic framework for both single-link and double-link connections between the tiles. For single-link connections, three Archimedean tilings considered as hinged body-bar frameworks are found here to be equiauxetic: these are {3.122}, {4.6.12}, and {4.82}. For double-link connections, three Archimedean tilings considered as hinged body-bar frameworks are found to be equiauxetic: these are {34.6}, {32.4.3.4}, and {3.6.3.6}.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
Keywords: | auxetic; tilings; symmetry; point group |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Science (Sheffield) > Department of Chemistry (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 16 Feb 2022 10:16 |
Last Modified: | 16 Feb 2022 10:16 |
Status: | Published |
Publisher: | MDPI AG |
Refereed: | Yes |
Identification Number: | 10.3390/sym14020232 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:183665 |