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Symmetry
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Metamaterials and Symmetry
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Metamaterials and Symmetry

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Chemistry: Symmetry/Asymmetry".

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 16192

Special Issue Editor

Dr. Teik-Cheng Lim

E-Mail Website
Guest Editor
School of Science and Technology, Singapore University of Social Sciences, Clementi Road, Singapore, Singapore
Interests: auxetics; auxetic materials; plates and shells
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Metamaterials are solids that are microstructured in such a manner that their overall behavior is predominantly determined by the geometrical properties of the microlattices rather than by the characteristics of the base materials. As a consequence, metamaterial properties can be pushed to extremal positive and negative values that well surpass the properties of naturally occurring materials, thereby opening up possibilities to design materials, structures and devices that have not been achievable until recently. Beyond the realms of physics and materials science, in which metamaterials have traditionally been investigated, modern research in metamaterials has penetrated the domains of chemistry, biology and even consumer products. This Special Issue is focused on the influence of symmetry and asymmetry of microarchitectures on the properties of metamaterials. Topics may include, but are not limited to, the following broad categories:

  • Acoustic and mechanical metamaterials;
  • Electromagnetic and optical metamaterials;
  • Metamaterials with extremal values;
  • Metamaterials with negative parameters.

Prof. Dr. Teik-Cheng Lim
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (7 papers)

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Editorial

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3 pages, 209 KiB  
Editorial
Metamaterials and Symmetry
by Teik-Cheng Lim
Symmetry 2022, 14(8), 1587; https://doi.org/10.3390/sym14081587 - 2 Aug 2022
Cited by 1 | Viewed by 987
Abstract
How are metamaterials related to symmetry [...] Full article
(This article belongs to the Special Issue Metamaterials and Symmetry)

Research

Jump to: Editorial

15 pages, 981 KiB  
Article
Equiauxetic Hinged Archimedean Tilings
by Tibor Tarnai, Patrick W. Fowler, Simon D. Guest and Flórián Kovács
Symmetry 2022, 14(2), 232; https://doi.org/10.3390/sym14020232 - 25 Jan 2022
Cited by 6 | Viewed by 2380
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 [...] Read more.
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}. Full article
(This article belongs to the Special Issue Metamaterials and Symmetry)
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33 pages, 28519 KiB  
Article
A Generalized Strain Energy-Based Homogenization Method for 2-D and 3-D Cellular Materials with and without Periodicity Constraints
by Ahmad I. Gad and Xin-Lin Gao
Symmetry 2021, 13(10), 1870; https://doi.org/10.3390/sym13101870 - 4 Oct 2021
Cited by 2 | Viewed by 1645
Abstract
A generalized strain energy-based homogenization method for 2-D and 3-D cellular materials with and without periodicity constraints is proposed using Hill’s Lemma and the matrix method for spatial frames. In this new approach, the equilibrium equations are enforced at all boundary and interior [...] Read more.
A generalized strain energy-based homogenization method for 2-D and 3-D cellular materials with and without periodicity constraints is proposed using Hill’s Lemma and the matrix method for spatial frames. In this new approach, the equilibrium equations are enforced at all boundary and interior nodes and each interior node is allowed to translate and rotate freely, which differ from existing methods where the equilibrium conditions are imposed only at the boundary nodes. The newly formulated homogenization method can be applied to cellular materials with or without symmetry. To illustrate the new method, four examples are studied: two for a 2-D cellular material and two for a 3-D pentamode metamaterial, with and without periodic constraints in each group. For the 2-D cellular material, an asymmetric microstructure with or without periodicity constraints is analyzed, and closed-form expressions of the effective stiffness components are obtained in both cases. For the 3-D pentamode metamaterial, a primitive diamond-shaped unit cell with or without periodicity constraints is considered. In each of these 3-D cases, two different representative cells in two orientations are examined. The homogenization analysis reveals that the pentamode metamaterial exhibits the cubic symmetry based on one representative cell, with the effective Poisson’s ratio v¯ being nearly 0.5. Moreover, it is revealed that the pentamode metamaterial with the cubic symmetry can be tailored to be a rubber-like material (with v¯ ≅0.5) or an auxetic material (with v¯ < 0). Full article
(This article belongs to the Special Issue Metamaterials and Symmetry)
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14 pages, 3841 KiB  
Article
Infinitesimal Periodic Deformations and Quadrics
by Ciprian S. Borcea and Ileana Streinu
Symmetry 2021, 13(9), 1719; https://doi.org/10.3390/sym13091719 - 17 Sep 2021
Cited by 1 | Viewed by 1481
Abstract
We describe a correspondence between the infinitesimal deformations of a periodic bar-and-joint framework and periodic arrangements of quadrics. This intrinsic correlation provides useful geometric characteristics. A direct consequence is a method for detecting auxetic deformations, identified by a pattern consisting of homothetic ellipsoids. [...] Read more.
We describe a correspondence between the infinitesimal deformations of a periodic bar-and-joint framework and periodic arrangements of quadrics. This intrinsic correlation provides useful geometric characteristics. A direct consequence is a method for detecting auxetic deformations, identified by a pattern consisting of homothetic ellipsoids. Examples include frameworks with higher crystallographic symmetry. Full article
(This article belongs to the Special Issue Metamaterials and Symmetry)
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21 pages, 11979 KiB  
Article
Extreme Poisson’s Ratios of Honeycomb, Re-Entrant, and Zig-Zag Crystals of Binary Hard Discs
by Mikołaj Bilski, Paweł M. Pigłowski and Krzysztof W. Wojciechowski
Symmetry 2021, 13(7), 1127; https://doi.org/10.3390/sym13071127 - 24 Jun 2021
Cited by 13 | Viewed by 2893
Abstract
Two-dimensional (2D) crystalline structures based on a honeycomb geometry are analyzed by computer simulations using the Monte Carlo method in the isobaric-isothermal ensemble. The considered crystals are formed by hard discs (HD) of two different diameters which are very close to each other. [...] Read more.
Two-dimensional (2D) crystalline structures based on a honeycomb geometry are analyzed by computer simulations using the Monte Carlo method in the isobaric-isothermal ensemble. The considered crystals are formed by hard discs (HD) of two different diameters which are very close to each other. In contrast to equidiameter HD, which crystallize into a homogeneous solid which is elastically isotropic due to its six-fold symmetry axis, the systems studied in this work contain artificial patterns and can be either isotropic or anisotropic. It turns out that the symmetry of the patterns obtained by the appropriate arrangement of two types of discs strongly influences their elastic properties. The Poisson’s ratio (PR) of each of the considered structures was studied in two aspects: (a) its dependence on the external isotropic pressure and (b) in the function of the direction angle, in which the deformation of the system takes place, since some of the structures are anisotropic. In order to accomplish the latter, the general analytic formula for the orientational dependence of PR in 2D systems was used. The PR analysis at extremely high pressures has shown that for the vast majority of the considered structures it is approximately direction independent (isotropic) and tends to the upper limit for isotropic 2D systems, which is equal to +1. This is in contrast to systems of equidiameter discs for which it tends to 0.13, i.e., a value almost eight times smaller. Full article
(This article belongs to the Special Issue Metamaterials and Symmetry)
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19 pages, 2561 KiB  
Article
Shearing Deformations of β-Cristobalite-Like Boron Arsenate
by James N. Grima-Cornish, Liana Vella-Żarb, Krzysztof W. Wojciechowski and Joseph N. Grima
Symmetry 2021, 13(6), 977; https://doi.org/10.3390/sym13060977 - 31 May 2021
Cited by 9 | Viewed by 2015
Abstract
Boron arsenate, BAsO4, is crystalline material (I4¯ group) that was recently shown to be auxetic in its (001) plane for loading in any direction in this plane, and, which exhibits negative linear compressibility at elevated pressured in its [...] Read more.
Boron arsenate, BAsO4, is crystalline material (I4¯ group) that was recently shown to be auxetic in its (001) plane for loading in any direction in this plane, and, which exhibits negative linear compressibility at elevated pressured in its [001] direction. This work presents and discusses the results of extensive density functional theory (DFT) based simulations aimed at studying deformations that such crystals undergo when subjected to shear loading in an attempt to obtain a better insight into the manner in which this material responds to mechanical loads. The deformations for shearing in the (001) plane are described in terms of the ‘rotating squares’ model, which was used to explain the auxeticity in the same plane where it was shown that shear loading results primarily in deformations which make the ‘squares’ become ‘parallelogram-like’ rather than rotate. This lack of rigidity in projected ‘squares’ was discussed by looking at changes in bond lengths and bond angles. Full article
(This article belongs to the Special Issue Metamaterials and Symmetry)
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14 pages, 6389 KiB  
Article
An Auxetic System Based on Interconnected Y-Elements Inspired by Islamic Geometric Patterns
by Teik-Cheng Lim
Symmetry 2021, 13(5), 865; https://doi.org/10.3390/sym13050865 - 12 May 2021
Cited by 12 | Viewed by 2681
Abstract
A 2D mechanical metamaterial exhibiting perfectly auxetic behavior, i.e., Poisson’s ratio of −1, is proposed in this paper drawing upon inspiration from an Islamic star formed by circumferential arrangement of eight squares, such as the one found at the exterior of [...] Read more.
A 2D mechanical metamaterial exhibiting perfectly auxetic behavior, i.e., Poisson’s ratio of −1, is proposed in this paper drawing upon inspiration from an Islamic star formed by circumferential arrangement of eight squares, such as the one found at the exterior of the Ghiyathiyya Madrasa in Khargird, Iran (built 1438–1444 AD). Each unit of the metamaterial consists of eight pairs of pin-jointed Y-shaped rigid elements, whereby every pair of Y-elements is elastically restrained by a spiral spring. Upon intermediate stretching, each metamaterial unit resembles the north dome of Jameh Mosque, Iran (built 1087–1088 AD), until the attainment of the fully opened configuration, which resembles a structure in Agra, India, near the Taj Mahal. Both infinitesimal and finite deformation models of the effective Young’s modulus for the metamaterial structure were established using strain energy approach in terms of the spiral spring stiffness and geometrical parameters, with assumptions to preserve the eight-fold symmetricity of every metamaterial unit. Results indicate that the prescription of strain raises the effective Young’s modulus in an exponential manner until full extension is attained. This metamaterial is useful for applications where the overall shape of the structure must be conserved in spite of uniaxial application of load, and where deformation is permitted under limited range, which is quickly arrested as the deformation progresses. Full article
(This article belongs to the Special Issue Metamaterials and Symmetry)
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