Composite metamaterial square grids with sign-flipping expansion coefficients leading to a type of Islamic design
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Composite metamaterial square grids with sign‑flipping expansion coefficients leading to a type of Islamic design Teik‑Cheng Lim1 Received: 25 February 2020 / Accepted: 7 April 2020 © Springer Nature Switzerland AG 2020
Abstract A class of 2D metamaterials with sign-switching coefficients of thermal, pressure and moisture expansions is proposed herein—such materials not only change properties with environmental changes, but also reverses between positive and negative. Designed from bimaterial strips and arranged into the form of square grids, changes to environmental conditions transform the square grids into 2D array of 8-pointed stars found in Islamic art and architecture. Results indicate that the bimaterial strip deflection can fit the 8-pointed star when the overall strain is−0.105 . Suppose the general expansion coefficients for both materials in the bimaterial strip (𝛼1 , 𝛼2 ) are known, then the required environmental changes for attaining the 8-pointed star array can be determined. The currently proposed metamaterial not only demonstrates its capability of attaining properties with reversible sign, but also achieve aesthetic feature with historical significance. Keywords Environmental change · Islamic art · Metamaterials · Sign-toggling List of symbols 𝛼 Generic coefficient of environmental expansion 𝛼1 Generic coefficient of environmental expansion for material 1 of bimaterial strip 𝛼2 Generic coefficient of environmental expansion for material 2 of bimaterial strip 𝛼V(C) Volumetric coefficient of moisture expansion 𝛼 (C) Linear coefficient of moisture expansion 𝛼V(T ) Volumetric coefficient of thermal expansion 𝛼 (T ) Linear coefficient of thermal expansion 𝛼V(P): Compressibility, or the coefficient of compressibility 𝛼 (P) Linear coefficient of compressibility 𝜀C Strain due to change in moisture concentration 𝜀P Strain due to pressure change 𝜀T Strain due to temperature change C Moisture concentration E1 Young’s modulus of material 1 in bimaterial strip E2 Young’s modulus of material 2 in bimaterial strip h Thickness of bimaterial strip
h1 Thickness of material 1 in bimaterial strip h2 Thickness of material 2 in bimaterial strip I1 Second moment area of material 1 in bimaterial strip I2 Second moment area of material 2 in bimaterial strip K Bulk modulus L Generalized length l Length of a segment of bimaterial m Moisture mass in solid M Mass of dry solid P Pressure r Radius of curvature of a bimaterial due to environmental change T Temperature V Volume
* Teik‑Cheng Lim, [email protected] | 1School of Science and Technology, Singapore University of Social Sciences, Singapore, Singapore. SN Applied Sciences
(2020) 2:918
| https://doi.org/10.1007/s42452-020-2725-0
Vol.:(0123456789)
Research Article
SN Applied Sciences
(2020) 2:918
1 Introduction Metamaterials are artificially-designed materials possessing characteristics that do not exist naturally. Such physical behavior arise from the architectured microstructure and not due to the base material properties.
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