Composite metamaterial square grids with sign-flipping expansion coefficients leading to a type of Islamic design

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 (1 , 2) 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 Generic coefficient of environmental expansion 1 Generic coefficient of environmental expansion for material 1 of bimaterial strip 2 Generic coefficient of environmental expansion for material 2 of bimaterial strip (C) V

A perfect 2D auxetic sliding mechanism based on an Islamic geometric pattern

“…A mechanism that is less explored is that of sliding mechanism, which was first presented by Wojciechowski and Branka [49] and later the aspect of negative stiffness was included by Lakes and Wojciechowski [50], as well as related works [51][52][53]. Of late, a few microstructural patterns with counter-intuitive properties have been designed based on inspiration from Islamic motifs [54][55][56][57]. This paper explores the use of sliding mechanism on a type of interconnected 8-pointed and 4-pointed stars that resemble a type of Islamic geometric pattern.…”

An Auxetic System Based on Interconnected Y-Elements Inspired by Islamic Geometric Patterns

“…This means that upon application of uniaxial tension or uniaxial compression a two-dimensional system undergoes equi-biaxial strain while a three-dimensional system undergoes equi-triaxial strain, so that the overall shape is conserved. Of late, the fields of auxetic and other metamaterials have been enriched by inspiration from Islamic motifs [42][43][44][45][46]. In addition, there have been recent works that appraise the various symmetry aspects of auxetic systems [47][48][49][50][51][52].…”

An Auxetic Metamaterial with Tunable Positive to Negative Hygrothermal Expansion by means of Counter‐Rotating Crosses

“…In a departure from recent mechanical metamaterials that have been inspired by Islamic geometrical patterns, [68][69][70][71][72] this article draws inspiration from the cross symbol for developing a metamaterial, in which its coefficient of thermal expansion (CTE) and coefficient of moisture expansion (CME) can be tuned DOI: 10.1002/pssb.202100137 A type of mechanical metamaterial is proposed, whereby the effective coefficients of thermal and moisture expansions (CTE and CME, respectively) can be tuned from positive to negative values while maintaining a consistently auxetic (negative Poisson's ratio) behavior for the overall structure. Each unit consists of a pair of equal-armed crosses pin jointed at their centers, whereas their ends are connected via bridging beams using pin joints to facilitate free rotation.…”