Element contents
A Partially Auxetic Metamaterial Inspired by the Maltese Cross
Published online by Cambridge University Press: 25 August 2022
Summary
A partially-auxetic metamaterial is introduced, inspired by the Maltese cross. Each unit of this metamaterial consists of a pair of counter-rotating equal-armed crosses, which is interconnected to neighboring units via hinge rods and connecting rods. Based on linkage theory, the on-axes Poisson's ratio was established considering a two-fold symmetrical mechanism, while the (anti)tetrachiral mechanisms were identified for on-axes uniaxial compression. A shearing mechanism is suggested for pure shearing and diagonal loading of the metamaterial with square array. Results suggest that the approximated infinitesimal models are valid for the Poisson's ratio of the two-fold symmetrical and the (anti)tetrachiral mechanisms under on-axis tension and compression, respectively; however, the finite model is recommended for quantifying the Poisson's ratio under pure shear and off-axis loading. This metamaterial manifests microstructural trinity, in which three different loading modes result in three different groups of deformation mechanisms. Finally, suggestions are put forth for some unsolved predictive problems.
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- Online ISBN: 9781009246415Publisher: Cambridge University PressPrint publication: 15 September 2022
References
Pendry, JB (2000), Negative refraction makes a perfect lens, Phys. Rev. Lett., 85(18), 3966–3969.CrossRefGoogle ScholarPubMed
Caloz, C and Itoh, T (2006), Electromagnetic Metamaterials: Transmission Line Theory and Microwave Applications. Wiley, Hoboken, NJ.Google Scholar
Grimberg, R (2013), Electromagnetic metamaterials, Mater. Sci. Eng. B, 178(19), 1285–1295.Google Scholar
Cui, TJ, Tang, WX, Yang, XM, Mei, ZL, and Jiang, WX (2016), Metamaterials: Beyond Crystals, Noncrystals, and Quasicrystals. CRC Press, Boca Raton, FL.Google Scholar
Fang, N, Xi, D, Xu, J, Ambati, M, Srituravanich, W, Sun, C, and Zhang, X (2006), Ultrasonic metamaterials with negative modulus, Nat. Mater., 5(6), 452–456.Google Scholar
Pendry, JB and Li, J (2008), An acoustic metafluid: Realizing a broadband acoustic cloak, New J. Phys., 10(11), 115032.CrossRefGoogle Scholar
Milton, GW, Briane, M, and Willis, JR (2006), On cloaking for elasticity and physical equations with a transformation invariant form, New J. Phys., 8(10), 248.CrossRefGoogle Scholar
Frenzel, T, Kadic, M, and Wegener, M (2017), Three-dimensional mechanical metamaterials with a twist, Science, 358(6366), 1072–1074.CrossRefGoogle ScholarPubMed
Sujardi, JU, Gao, L, Du, H, Li, X, Xiong, X, Fang, NX, and Lu, Y (2019), Mechanical metamaterials and their engineering applications, Adv. Eng. Mater., 21(3), 1800864.Google Scholar
Huidobro, PA, Fernandez-Dominguez, AI, Pendry, JB, Martin-Moreno, L, and Garcia-Vidal, FJ (2018), Spoof Surface Plasmon Metamaterials. Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Li, R, Wang, Z, and Chen, H (2020), Metamaterials and Negative Refraction. Cambridge University Press, Cambridge.Google Scholar
Cui, TJ and Liu, S (2021), Information Metamaterials. Cambridge University Press, Cambridge.Google Scholar
Jiang, WX, Mei, ZL, and Cui, TJ (2021), Effective Medium Theory of Metamaterials and Metasurfaces. Cambridge University Press, Cambridge.Google Scholar
Li, Y, Zhou, Z, He, Y, and Li, H (2021), Epsilon-Near-Zero Metamaterials. Cambridge University Press, Cambridge.Google Scholar
Hummel, FA (1951), Thermal expansion properties of some synthetic lithia minerals, J. Am. Ceram. Soc., 34(8), 235–239.CrossRefGoogle Scholar
Chu, CN, Saka, N, and Suh, NP (1987), Negative thermal expansion ceramics: A review, Mater. Sci. Eng., 95, 303–308.Google Scholar
Sleight, AW (1998), Compounds that contract on heating, Inorg. Chem., 37(12), 2854–2860.CrossRefGoogle Scholar
Sleight, AW (1998), Isotropic negative thermal expansion, Ann. Rev. Mater. Sci., 28, 29–43.CrossRefGoogle Scholar
Mary, TA, Evans, JSO, Vogt, T, and Sleight, AW (1996), Negative thermal expansion from 0.3 to 1050 Kelvins in ZrW2O8, Science, 272(5258), 90–92.Google Scholar
Dove, MT, Welche, PRL, and Heine, V (1998), Negative thermal expansion in beta-quartz, Phys. Chem. Minerals, 26(1), 63–77.Google Scholar
Evans, JSO, Hanson, JC, and Sleight, AW (1998), Room-temperature superstructure of ZrV2O7, Acta Crystallog. B, 54(6), 705–713.CrossRefGoogle Scholar
Evans, JSO, Jorgensen, JD, Short, S, David, WIF, Ibberson, RM, and Sleight, AW (1999), Thermal expansion in the orthorhombic phase of ZrW2O8, Phys. Rev. B, 60(21), 14643–14648.Google Scholar
Lim, TC (2005), Anisotropic and negative thermal expansion behavior in a cellular microstructure, J. Mater. Sci., 40(12), 3275–3277.CrossRefGoogle Scholar
Barrera, GD, Bruno, JAO, Barron, THK, and Allan, NL (2005), Negative thermal expansion, J. Phys.: Condens. Matter, 17(4), R217–R252.Google Scholar
Miller, W, Smith, CW, Mackenzie, DS, and Evans, KE (2009), Negative thermal expansion: A review, J. Mater. Sci., 44(20), 5441–5451.Google Scholar
Lim, TC (2012), Negative thermal expansion structures constructed from positive thermal expansion trusses, J. Mater. Sci., 47(1), 368–373.Google Scholar
Lim, TC (2013), Negative thermal expansion in transversely isotropic space frame trusses, Phys. Status Solidi B, 250(10), 2062–2069.Google Scholar
Lim, TC (2017), Auxetic and negative thermal expansion structure based on interconnected array of rings and sliding rods, Phys. Status Solidi B, 254(12), 1600775.Google Scholar
Attfield, JP (2018), Mechanisms and materials for NTE, Front. Chem., 6, 371.CrossRefGoogle ScholarPubMed
Ai, L and Gao, XL (2018), Three-dimensional metamaterials with a negative Poisson’s ratio and a non-positive coefficient of thermal expansion, Int. J. Mech. Sci., 135, 101–113.Google Scholar
Takenaka, K (2018), Progress of research in negative thermal expansion materials: Paradigm shift in the control of thermal expansion, Front. Chem., 6, 267.CrossRefGoogle ScholarPubMed
Lim, TC (2019), A 2D auxetikos system based on interconnected shurikens, SN Appl. Sci., 1(11), 1383.Google Scholar
Lim, TC (2019), 2D metamaterial with in-plane positive and negative thermal expansion and thermal shearing based on interconnected alternating bimaterials, Mater. Res. Exp., 6(11), 115804.Google Scholar
Lim, TC (2020), Metacomposite with auxetic and in situ sign reversible thermal expansivity upon temperature fluctuation, Compos. Commun., 19, 30–36.CrossRefGoogle Scholar
Baughman, RH, Stafstrom, S, Cui, C, and Dantas, SO (1998), Materials with negative compressibilities in one or more dimensions, Science, 279(5356), 1522–1524.Google Scholar
Gatt, R and Grima, JN (2008), Negative compressibility, Phys. Status Solidi RRL, 2(5), 236–238.Google Scholar
Goodwin, AL, Keen, DA, and Tucker, MG (2008), Large negative linear compressibility of Ag3[Co(CN)6], Proc. Nat. Acad. Sci., 105(48), 18708–18713.CrossRefGoogle ScholarPubMed
Lakes, R and Wojciechowski, KW (2008), Negative compressibility, negative Poisson’s ratio, and stability, Phys. Status Solidi B, 245(3), 545–551.Google Scholar
Grima, JN, Attard, D, and Gatt, R (2008), Truss‐type systems exhibiting negative compressibility, Phys. Status Solidi B, 245(11), 2405–2414.Google Scholar
Fortes, ADS, Suard, E, and Knight, KS (2011), Negative linear compressibility and massive anisotropic thermal expansion in methanol monohydrate, Science, 331(6018), 742–746.Google Scholar
Grima, JN, Attard, D, Caruana-Gauci, R, and Gatt, R (2011), Negative linear compressibility of hexagonal honeycombs and related systems, Scripta Mater., 65(7), 565–568.Google Scholar
Grima, JN, Caruana-Gauci, R, Attard, D, and Gatt, R (2012), Three-dimensional cellular structures with negative Poisson’s ratio and negative compressibility properties, Proc. Royal Soc. A, 468(2146), 3121–3138.Google Scholar
Nicolaou, ZG and Motter, AE (2012), Mechanical metamaterials with negative compressibility transitions, Nat. Mater., 11(7), 608–613.Google Scholar
Cairns, AB, Catafesta, J, Levelut, C, Rouquette, J, van der Lee, A, Peters, L, Thompson, AL, Dmitriev, V, Haines, J, and Goodwin, AL (2013), Giant negative linear compressibility in zinc dicyanoaurate, Nat. Mater., 12(3), 212–216.Google Scholar
Grima, JN, Caruana-Gauci, R, Wojciechowski, KW, and Evans, KE (2013), Smart hexagonal truss systems exhibiting negative compressibility through constrained angle stretching, Smart Mater. Struct., 22(8), 084015.CrossRefGoogle Scholar
Imre, AR (2014), Metamaterials with negative compressibility – a novel concept with a long history, Mater. Sci.-Poland, 32(2), 126–129.CrossRefGoogle Scholar
Miller, W, Evans, KE, and Marmier, A (2015), Negative linear compressibility in common materials, Appl. Phys. Lett., 106(23), 231903.Google Scholar
Cairns, AB and Goodwin, AL (2015), Negative linear compressibility, Phys. Chem. Chem. Phys., 17(32), 20449–20465.Google Scholar
Zhou, X, Zhang, L, Zhang, H, Liu, Q, and Ren, T (2016), 3D cellular models with negative compressibility through the wine-rack-type mechanism, Phys. Status Solidi B, 253(10), 1977–1993.CrossRefGoogle Scholar
Attard, D, Caruana-Gauci, R, Gatt, R, and Grima, JN (2016), Negative linear compressibility from rotating rigid units, Phys. Status Solidi B, 253(7), 1410–1418.CrossRefGoogle Scholar
Dudek, KK, Attard, D, Caruana-Gauci, R, Wojciechowski, KW, and Grima, JN (2016), Unimode metamaterials exhibiting negative linear compressibility and negative thermal expansion, Smart Mater. Struct., 25(2), 025009.Google Scholar
Lim, TC (2017), 2D structures exhibiting negative area compressibility, Phys. Status Solidi B, 254(12), 1600682.Google Scholar
Colmenero, F (2019), Silver oxalate: mechanical properties and extreme negative mechanical phenomena, Adv. Theory Simul., 2(6), 1900040.Google Scholar
Degabriele, EP, Attard, D, Grima-Cornish, JN, Caruana-Gauci, R, Gatt, R, Evans, KE, and Grima, JN (2019), On the compressibility properties of the wine-rack-like carbon allotropes and related poly(phenylacetylene), Phys. Status Solidi B, 256(1), 1800572.Google Scholar
Grima-Cornish, JN, Grima, JN, and Attard, D (2020), A novel mechanical metamaterial exhibiting auxetic behavior and negative compressibility, Materials, 13(1), 79.CrossRefGoogle Scholar
Barrett, DG, Bushnell, GG, and Messersmith, PB (2013), Mechanically robust, negative-swelling, mussel-inspired tissue adhesives, Adv. Healthcare Mater., 2(5), 745–755.Google Scholar
Liu, J, Gu, T, Shan, S, Kang, SH, Weaver, JC, and Bertoldi, K (2016), Harnessing buckling to design architected materials that exhibit effective negative swelling, Adv. Mater., 28(31), 6619–6624.CrossRefGoogle ScholarPubMed
Lim, TC (2018), A negative hygroscopic expansion material, Mater. Sci. Forum., 928, 277–282.CrossRefGoogle Scholar
Curatolo, M (2018), Effective negative swelling of hydrogel-solid composites, Extreme Mech. Lett., 25, 46–52.CrossRefGoogle Scholar
Zhang, H, Gou, X, Wu, J, Fang, D, and Zhang, Y (2018), Soft mechanical metamaterials with unusual swelling behavior and tunable stress-strain curves, Sci. Adv., 4 (6), eaar8535.Google Scholar
Lim, TC (2019), A reinforced kite-shaped microstructure with negative linear and area hygrothermal expansions, Key Eng. Mater., 803, 272–277.Google Scholar
Lim, TC (2019), Negative environmental expansion for interconnected array of rings and sliding rods, Phys. Status Solidi B, 256(1), 1800032.Google Scholar
Lim, TC (2020), Negative hygrothermal expansion of reinforced double arrowhead microstructure, Phys. Status Solidi B, 257(10), 1800055.Google Scholar
Lakes, RS (1993), Microbuckling instability in elastomeric cellular solids, J. Mater. Sci., 28(17), 4667–4672.Google Scholar
Wang, YC and Lakes, RS (2001), Extreme thermal expansion, piezoelectricity, and other coupled field properties in composites with a negative stiffness phase, J. Appl. Phys., 90(12), 6458–6465.Google Scholar
Lakes, RS (2001), Extreme damping in compliant composites with a negative-stiffness phase, Phil. Mag. Lett., 81(2), 95–100.Google Scholar
Lakes, RS (2001), Extreme damping in composite materials with a negative stiffness phase, Phys. Rev. Lett., 86(13), 2897–2900.Google Scholar
Lakes, RS, Lee, T, Bersie, A, and Wang, YC (2001), Extreme damping in composite materials with negative stiffness inclusions, Nature, 410(6828), 565–567.Google Scholar
Lakes, RS and Drugan, WJ (2002), Dramatically stiffer elastic composite materials due to a negative stiffness phase?, J. Mech. Phys. Solids, 50(5), 979–1009.Google Scholar
Wang, YC and Lakes, RS (2004), Extreme stiffness systems due to negative stiffness elements, Am. J. Phys., 72(1), 40–50.Google Scholar
Wang, YC and Lakes, RS (2004), Negative stiffness-induced extreme viscoelastic mechanical properties: Stability and dynamics, Phil. Mag., 84(35), 3785–3801.Google Scholar
Wang, YC and Lakes, RS (2005), Stability of negative stiffness viscoelastic systems, Quart. Appl. Math., 63(1), 34–55.Google Scholar
Wang, YC, Swadener, JG, and Lakes, RS (2006), Two-dimensional viscoelastic discrete triangular system with negative-stiffness components, Phil. Mag. Lett., 86(2), 99–112.Google Scholar
Moore, B, Jaglinski, T, Stone, DS, and Lakes, RS (2006), Negative incremental bulk modulus in foams, Phil. Mag. Lett., 86(10), 651–659.Google Scholar
Dyskin, AV and Pasternak, E (2012), Mechanical effect of rotating non-spherical particles on failure in compression, Phil. Mag., 92(28–30), 3451–3473.Google Scholar
Rafsanjani, A, Akbarzadeh, A, and Pasini, D (2015), Snapping mechanical metamaterials under tension, Adv. Mater., 27(39), 5931–5935.Google Scholar
Balch, SP and Lakes, RS (2017), Amelioration of waves and microvibrations by micro-buckling in open celled foam, Cell. Polym., 36(1), 1–12.Google Scholar
Che, K, Yuan, C, Wu, J, Qi, HJ, and Meaud, J (2017), Three-dimensional-printed multistable mechanical metamaterials with a deterministic deformation sequence, J. Appl. Mech., 84(1), 011004.Google Scholar
Dudek, KK, Gatt, R, Dudek, MR, and Grima, JN (2018), Negative and positive stiffness in auxetic magneto-mechanical metamaterials, Proc. Royal Soc. A, 474(2215), 20180003.Google Scholar
Ha, CS, Lakes, RS, and Plesha, ME (2018), Design, fabrication, and analysis of lattice exhibiting absorption via snap through behaviour, Mater. Des., 141, 426–437.Google Scholar
Ha, CS, Lakes, RS, and Plesha, ME (2019), Cubic negative stiffness lattice structure for energy absorption: Numerical and experimental studies, Int. J. Solids Struct., 178–179, 127–135.Google Scholar
Karachevtseva, I, Pasternak, E, and Dyskin, AV (2019), Negative stiffness produced by rotation of non‐spherical particles and its effect on frictional sliding, Phys. Status Solidi B, 256(1), 1800003.Google Scholar
Pasternak, E and Dyskin, AV (2019), Architectured materials with inclusions having negative Poisson’s ratio or negative stiffness. In Estrin, Y, Brechet, Y, Dunlop, J, and Fratzl, P (eds.), Architectured Materials in Nature and Engineering, pp. 51–87. Springer Nature, Cham.Google Scholar
Wang, YC, Lai, HW, and Shen, MW (2019), Effects of cracks on anomalous mechanical behavior and energy dissipation of negative-stiffness plates, Phys. Status Solidi B, 256(1), 1800489.Google Scholar
Zhang, Y, Restrepo, D, Velay-Lizancos, M, Mankame, ND, and Zavattieri, PD (2019), Energy dissipation in functionally two-dimensional phase transforming cellular materials, Scient. Rep., 9, 12581.Google Scholar
Evans, KE, Nkansah, MA, Hutchinson, IJ, and Rogers, SC (1991), Molecular design network, Nature, 353(6340), 124.Google Scholar
Simmons, G and Birch, F (1963), Elastic constants of pyrite, J. Appl. Phys., 34(9), 2736–2738.Google Scholar
Benbattouche, N, Saunders, GA, Lambson, EF, and Honle, W (1989), The dependences of the elastic stiffness moduli and the Poisson ratio of natural iron pyrites FeS2 upon pressure and temperature, J. Phys. D. Appl. Phys., 22(5), 670–675.Google Scholar
Li, Y (1976), The anisotropic behavior of Poisson’s ratio, Young’s modulus, and shear modulus in hexagonal material, Phys. Status Solidi, 38(1), 171–175.Google Scholar
Berlincourt, D and Jaffe, H (1958), Elastic and piezoelectric coefficients of single-crystal barium titanate, Phys. Rev., 111(1), 143–148.Google Scholar
Alderson, A and Evans, KE (2009), Deformation mechanisms leading to auxetic behaviour in the α-cristobalite and α-quartz structures of both silica and germania, J. Phys. Condens. Matter, 21(2), 25401.Google Scholar
Kittinger, E, Tichy, J, and Bertagnolli, E (1981), Example of a negative effective Poisson’s ratio, Phys. Rev. Lett., 47(10), 712–714.Google Scholar
Milstein, F and Huang, K (1979), Existence of a negative Poisson ratio in fcc crystals, Phys. Rev. B, 19(4), 2030–2033.Google Scholar
Baughman, RH, Shacklette, JM, Zakhidov, AA, and Stafström, S (1998), Negative Poisson’s ratios as a common feature of cubic metals, Nature, 392(6674), 362–365.Google Scholar
Ho, DT, Park, SD, Kwon, SY, Park, K, and Kim, SY (2014), Negative Poisson’s ratios in metal nanoplates, Nat. Commun., 5, 3255.Google Scholar
Gunton, DJ and Saunders, GA (1972), The Young’s modulus and Poisson’s ratio of arsenic, antimony and bismuth, J. Mater. Sci., 7(9), 1061–1068.Google Scholar
Yeganeh-Haeri, A, Weidner, DJ, and Parise, JB (1992), Elasticity of α-cristobalite: A silicon dioxide with a negative Poisson’s ratio, Science, 257(5070), 650–652.Google Scholar
Homand-Etienne, F and Houpert, R (1989), Thermally induced microcracking in granites: Characterization and analysis, Int. J. Rock Mech. Min. Sci., 26(2), 125–134.Google Scholar
Peura, M, Grotkopp, I, Lemke, H, Vikkula, A, Laine, J, Müller, M, and Serima, R (2006), Negative Poisson ratio of crystalline cellulose in kraft cooked Norway spruce, Biomacromol., 7(5), 1521–1528.Google Scholar
Nakamura, K, Wada, M, Kuga, S, and Okano, T (2004), Poisson’s ratio of cellulose Iβ and cellulose II, J. Polym. Sci. Part B Polym. Phys., 42(7), 1206–1211.Google Scholar
Yao, YT, Alderson, A, and Alderson, KL (2012), Towards auxetic nanofibres: Molecular modelling of auxetic behaviour in cellulose II, Behavior and Mechanics of Multifunctional Materials and Composites Proc. SPIE, 8342, 83421W.Google Scholar
Veronda, DR and Westmann, RA (1970), Mechanical characterization of skin-finite deformations, J. Biomech., 3(1), 111–124.Google Scholar
Lees, C, Vincent, JFV, and Hillerton, JE (1991), Poisson’s Ratio in skin, Biomed. Mater. Eng., 1(1), 19–23.Google Scholar
Song, F, Zhou, J, Xu, X, Xu, Y, and Bai, Y (2008), Effect of a negative Poisson ratio in the tension of ceramics, Phys. Rev. Lett., 100(24), 245502.Google Scholar
Williams, JL and Lewis, JL (1982), Properties and an anisotropic model of cancellous bone from the proximal tibial epiphysis, J. Biomech. Eng., 104(1), 50–56.Google Scholar
Renson, CE and Braden, M (1975), Experimental determination of the rigidity modulus, Poisson’s ratio and elastic limit in shear of human dentine, Arch. Oral Biol., 20(1), 43–47.Google Scholar
Schmidt, CF, Svoboda, K, Lei, N, Petsche, IB, Berman, LE, Safinya, CR, and Grest, G (1993), Existence of a flat phase in red cell membrane skeletons, Science, 259(5097), 952–955.Google Scholar
Chen, X and Brodland, GW (2009), Mechanical determinants of epithelium thickness in early-stage embryos, J. Mech. Behav. Biomed. Mater., 2(5), 494–501.Google Scholar
Timmins, LH, Wu, Q, Yeh, AT, Moore, JE, and Greenwald, SE (2010), Structural inhomogeneity and fiber orientation in the inner arterial media, Am. J. Physiol. Heart Circ. Physiol., 298(5), H1537–H1545.Google Scholar
Patten, K and Wess, T (2013), Suprafibrillar structures of collagen, evidence for local organization and auxetic behaviour in architectures, J. Biophys. Chem., 4(3), 103–109.Google Scholar
Pagliara, S, Franze, K, McClain, CR, Wylde, GW, Fisher, CL, Franklin, RJM, Kabla, AJ, Keyser, UF, and Chalut, KJ (2014), Auxetic nuclei in embryonic stem cells exiting pluripotency, Nat. Mater., 13(6), 638–644.Google Scholar
Tokmakova, SP (2005), Stereographic projections of Poisson’s ratio in auxetic crystals, Phys. Status Solidi B, 242(3), 721–729.Google Scholar
Grima, JN, Winczewski, S, Mizzi, L, Grech, MC, Cauchi, R, Gatt, R, Attard, D, Wojciechowski, KW, and Rybicki, J (2015), Tailoring graphene to achieve negative Poisson’s ratio properties, Adv. Mater., 27(8), 1455–1459.Google Scholar
Aouni, N and Wheeler, L (2008), Auxeticity of calcite and aragonite polymorphs of CaCO3 and crystals of similar structure, Phys. Status Solidi B, 245(11), 2454–2462.Google Scholar
Jiang, JW and Park, HS (2014), Negative Poisson’s ratio in single-layer black phosphorus, Nat. Commun., 5, 4727.Google Scholar
Jiang, JW, Rabczuk, T, and Park, HS (2015), A Stillinger–Weber potential for single-layered black phosphorus, and the importance of cross-pucker interactions for a negative Poisson’s ratio and edge stress-induced bending, Nanoscale, 7(14), 6059–6068.Google Scholar
Jiang, JW (2015), Thermal conduction in single-layer black phosphorus: Highly anisotropic?, Nanotechnol., 26(5), 055701.Google Scholar
Rovati, M (2003), On the negative Poisson’s ratio of an orthorhombic alloy, Scr. Mater., 48(3), 235–240.Google Scholar
Kellogg, RA, Russell, AM, Lograsso, TA, Flatau, AB, Clark, AE, and Wun-Fogle, M (2003), Mechanical properties of magnetostrictive iron-gallium alloys, SPIE Smart Structures and Materials 2003, Active Materials: Behaviour and Mechanics, Proc., 5053, 70.Google Scholar
Kellogg, RA, Russell, AM, Lograsso, TA, Flatau, AB, Clark, AE, and Wun-Fogle, M (2004), Tensile properties of magnetostrictive iron–gallium alloys, Acta Mater., 52(7), 5043–5050.Google Scholar
Petculescu, G, Hathaway, KB, Lograsso, TA, Wun-Fogle, M, and Clark, AE (2005), Magnetic field dependence of galfenol elastic properties, J. Appl. Phys., 97(10), 10M315.Google Scholar
Schurter, HM and Flatau, AB (2008), Elastic properties and auxetic behavior of Galfenol for a range of compositions, Behavior and Mechanics of Multifunctional and Composite Materials, Proc. SPIE, 6929, 69291U.Google Scholar
Valant, M, Axelsson, AK, Aguesse, F, and Alford, NM (2010), Molecular auxetic behavior of epitaxial co-ferrite spinel thin film, Adv. Funct. Mater., 20(4), 644–647.Google Scholar
Zhang, Y, Wu, R, Schurter, HM, and Flatau, AB (2010), Understanding of large auxetic properties of iron-gallium and iron-aluminum alloys, J. Appl. Phys., 108(2), 023513.Google Scholar
Li, D, Jaglinski, T, Stone, DS, and Lakes, RS (2012), Temperature insensitive negative Poisson’s ratios in isotropic alloys near a morphotropic phase boundary, Appl. Phys. Lett., 101(25), 251903.Google Scholar
Wang, XF, Jones, TE, Li W, and Zhou, YC (2012), Extreme Poisson’s ratios and their electronic origin in B2 CsCl-type AB intermetallic compounds, Phys. Rev. B, 85 (13), 134108.Google Scholar
Lim, TC (2007), On simultaneous positive and negative Poisson’s ratio laminates, Phys. Status Solidi B, 244(3), 910–918.Google Scholar
Lim, TC (2012), Mixed auxeticity of auxetic sandwich structures, Phys. Status Solidi B, 249(7), 1366–1372.Google Scholar
Lakes, R (1987), Foam structures with a negative Poisson’s ratio, Science, 235(4792), 1038–1040.Google Scholar
Chan, N and Evans, KE (1998), Indentation resilience of conventional and auxetic foams, J. Cell. Plast., 34(3), 231–260.Google Scholar
Scarpa, F, Yates, JR, Ciffo, LG, and Patsias, S (2002), Dynamic crushing of auxetic open-cell polyurethane foam, Proc. Inst. Mech. Eng. Part C: J. Mech. Eng. Sci., 216(12), 1153–1156.Google Scholar
Friis, EA, Lakes, RS, and Park, JB (1988), Negative Poisson’s ratio polymeric and metallic foams, J. Mater. Sci., 23(12), 4406–4414.Google Scholar
Chen, CP and Lakes, RS (1996), Micromechanical analysis of dynamic behavior of conventional and negative Poisson’s ratio foams, J. Eng. Mater. Technol., 118(3), 285–288.Google Scholar
Chan, N and Evans, KE (1999), The mechanical properties of conventional and auxetic foams. Part I: Compression and tension, J. Cell. Plast., 35(2), 130–165.Google Scholar
Chan, N and Evans, KE (1999), The mechanical properties of conventional and auxetic foams. Part II: Shear, J. Cell. Plast., 35(2), 166–183.Google Scholar
Bezazi, A and Scarpa, F (2007), Mechanical behaviour of conventional and negative Poisson’s ratio thermoplastic polyurethane foams under compressive cyclic loading, Int. J. Fatigue, 29(5), 922–930.Google Scholar
Bezazi, A and Scarpa, F (2009), Tensile fatigue of conventional and negative Poisson’s ratio open cell PU foams, Int. J. Fatigue, 31(3), 488–494.Google Scholar
Bezazi, A, Boukharouba, W, and Scarpa, F (2009), Mechanical properties of auxetic carbon/epoxy composites: Static and cyclic fatigue behaviour, Phys. Status Solidi B, 246(9), 2102–2110.Google Scholar
Lim, TC, Alderson, A, and Alderson, KL (2014), Experimental studies on the impact properties of auxetic materials, Phys. Status Solidi B, 251(2), 307–313.Google Scholar
Scarpa, F, Giacomin, J, Zhang, Y, and Pastorino, P (2005), Mechanical performance of auxetic polyurethane foam for antivibration glove applications, Cell. Polym., 24(5), 253–268.Google Scholar
Choi, JB and Lakes, R (1995), Analysis of elastic modulus of conventional foams and of re-entrant foam materials with a negative Poisson’s ratio, Int. J. Mech. Sci., 37(1), 51–59.Google Scholar
Scarpa, F, Giacomin, JA, Bezazi, A, and Bullough, WA (2006), Dynamic behavior and damping capacity of auxetic foam pads, Smart Structures and Materials 2006: Damping and Isolation, Proc. SPIE, 6169, 61690T.Google Scholar
Pastorino, P, Scarpa, F, Patsias, S, Yates, JR, Haake, SJ, and Ruzzene, M (2007), Strain rate dependence of stiffness and Poisson’s ratio of auxetic open cell PU foams, Phys. Status Solidi B, 244(3), 955–965.Google Scholar
Lowe, A and Lakes, RS (2000), Negative Poisson’s ratio foam as seat cushion material, Cell. Polym., 19(3), 157–167.Google Scholar
Lim, TC (2018), Auxeticity of concentric auxetic-conventional foam rods with high modulus interface adhesive, Materials, 11(2), 223.Google Scholar
Strek, AM (2010), Production and study of polyether auxetic foam, Mech. Control, 29(2), 78–87.Google Scholar
Bianchi, M, Scarpa, F, Banse, M, and Smith, CW (2011), Novel generation of auxetic open cell foams for curved and arbitrary shapes, Acta Mater., 59(2), 686–691.Google Scholar
Bianchi, M, Frontoni, S, Scarpa, F, and Smith, CW (2011), Density change during the manufacturing process of PU-PE open cell auxetic foams, Phys. Status Solidi B, 248(1), 30–38.Google Scholar
Alderson, K, Alderson, A, Ravirala, N, Simkins, V, and Davies, P (2012), Manufacture and characterisation of thin flat and curved auxetic foam sheets, Phys. Status Solidi B, 249(7), 1315–1321.Google Scholar
Alderson, KL and Evans, KE (1993), Strain-dependent behaviour of microporous polyethylene with a negative Poisson’s ratio, J. Mater. Sci., 28(15), 4092–4098.Google Scholar
Alderson, KL, Alderson, A, Webber, RS, and Evans, KE (1998), Evidence for uniaxial drawing in the fibrillated microstructure of auxetic microporous polymers, J. Mater. Sci. Lett., 17(16), 1415–1419.Google Scholar
Pickles, AP, Webber, RS, Alderson, KL, Neale, PJ, and Evans, KE (1995), The effect of the processing parameters on the fabrication of auxetic polyethylene, J. Mater. Sci., 30(16), 4059–4068.Google Scholar
Alderson, KL, Webber, RS, and Evans, KE (2007), Microstructural evolution in the processing of auxetic microporous polymers, Phys. Status Solidi B, 244(3), 828–841.Google Scholar
Ravirala, N, Alderson, A, Alderson, KL, and Davies, PJ (2005), Auxetic polypropylene films, Polym. Eng. Sci., 45(4), 517–528.Google Scholar
Ravirala, N, Alderson, KL, Davies, PJ, Simkins, VR, and Alderson, A (2006), Negative Poisson’s ratio polyester fibers, Text. Res. J., 76(7), 540–546.Google Scholar
Chirima, GT, Zied, KM, Ravirala, N, Alderson, KL, and Alderson, A (2009), Numerical and analytical modelling of multi-layer adhesive-film interface systems, Phys. Status Solidi B, 246(9), 2072–2082.Google Scholar
Evans, KE (1991), Auxetic polymers: A new range of materials, Endeavour, 15(4), 170–174.Google Scholar
Alderson, KL, Pickles, AP, Neale, PJ, and Evans, KE (1994), Auxetic polyethylene: The effect of a negative Poisson’s ratio on hardness, Acta Metall. Mater., 42(7), 2261–2266.Google Scholar
Franke, M and Magerle, R (2011), Locally auxetic behavior of elastomeric polypropylene on the 100 nm length scale, ACS Nano, 5(6), 4886–4891.Google Scholar
Baker, J, Douglass, A, and Griffin, A (1995), Trimeric liquid crystals: Model compounds for auxetic polymer, ACS-Polym. Prepr., 36(2), 345–346.Google Scholar
Liu, P, He, C, and Griffin, A (1998), Liquid crystalline polymers as potential auxetic materials: Influence of transverse rods on the polymer mesophase, Abstr. Pap. Am. Chem. Soc., 216, 108.Google Scholar
He, C, Liu, P, and Griffin, A (1998), Toward negative Poisson ratio polymers through molecular design, Macromol., 31(9), 3145–3147, 1998.Google Scholar
He, C, Liu, P, Griffin, A, Smith, CW, and Evans, KE (2005), Morphology and deformation behaviour of a liquid crystalline polymer containing laterally attached pentaphenyl rods, Macromol. Chem. Phys., 206(2), 233–239.Google Scholar
He, C, Liu, P, McMullan, PJ, and Griffin, AC (2005), Toward molecular auxetics: Main chain liquid crystalline polymers consisting of laterally attached para-quaterphenyls, Phys. Status Solidi B, 242, 576–584.Google Scholar
Li, C, Xie, X, and Cao, S (2002), Synthesis and characterization of liquid crystalline copolyesters containing horizontal and lateral rods in main chain, Polym. Adv. Technol., 13(3–4), 178–187.Google Scholar
Dey, S, Agra-Kooijman, DM, Ren, W, McMullan, PJ, Griffin, AC, and Kumar, S (2013), Soft elasticity in main chain liquid crystal elastomers, Crystals, 3(2), 363–390.Google Scholar
Baughman, RH and Galvao, DS (1993), Crystalline networks with unusual predicted mechanical and thermal properties, Nature, 365(6448), 735–737.Google Scholar
Baughman, RH, Galvao, DS, Cui, C, and Dantas, S (1997), Hinged and chiral polydiacetylene carbon crystals, Chem. Phys. Lett., 269(3–4), 356–364.Google Scholar
Nkansah, MA, Evans, KE, and Hutchinson, IJ (1994), Modelling the mechanical properties of an auxetic molecular network, Model. Simul. Mater. Sci. Eng., 2(3), 337–352.Google Scholar
Grima, JN and Evans, KE (2000), Self-expanding molecular networks, Chem. Comm., 2000(16), 1531–1532.Google Scholar
Grima, JN (2008), On the mechanical properties and auxetic potential of various organic networked polymers, Mol. Simul., 34(10–15), 1149–1158.Google Scholar
Wen, X, Garland, CW, Hwa, T, Kardar, M, Kokufuta, E, Li, Y, Orkisz, M, and Tanaka, T (1992), Crumpled and collapsed conformation in graphite oxide membranes, Nature, 355(6359), 426–428.Google Scholar
Pour, N, Itzhaki, L, Hoz, B, Altus, E, Basch, H, and Hoz, S (2006), Auxetics at the molecular level: A negative Poisson’s ratio in molecular rods, Angew. Chemie, 45(36), 5981–5983.Google Scholar
Pour, N, Altus, E, Basch, H, and Hoz, S (2009), The origin of the auxetic effect in prismanes: Bowtie structure and the mechanical properties of biprismanes, J. Phys. Chem. C, 113(9), 3467–3470.Google Scholar
Hall, LJ, Coluci, VR, Galvao, DS, Kozlov, ME, Dantas, SO, and Baughman, RH (2008), Sign change of Poisson’s ratio for carbon nanotube sheets, Science, 320(5875), 504–507.Google Scholar
Yao, YT, Alderson, A, and Alderson, KL (2008), Can nanotubes display auxetic behaviour?, Phys. Status Solidi B, 245(11), 2373–2382.Google Scholar
Chen, L, Liu, C, Wang, J, Zhang, W, Hu, C, and Fan, S (2009), Auxetic materials with large negative Poisson’s ratios based on highly oriented carbon nanotube structures, Appl. Phys. Lett., 94(25), 253111.Google Scholar
Scarpa, F, Adhikari, S, and Srikantha Phani, A (2009), Effective elastic mechanical properties of single layer graphene sheets, Nanotechnol., 20(6), 065709.Google Scholar
Braghin, FL and Hasselmann, N (2010), Thermal fluctuations of free-standing graphene, Phys. Rev. B, 82(3), 035407.Google Scholar
Cadelano, E, Palla, PL, Giordano, S, and Colombo, L (2010), Elastic properties of hydrogenated graphene, Phys. Rev. B, 82(23), 235414.Google Scholar
Sihn, S, Varshney, V, Roy, AK, and Farmer, BL (2012), Prediction of 3D elastic moduli and Poisson’s ratios of pillared graphene nanostructures, Carbon, 50(2), 603–611.Google Scholar
Koskinen, P (2014), Graphene cardboard: From ripples to tunable metamaterial, Appl. Phys. Lett., 104(10), 101902.Google Scholar
Grima, JN, Jackson, R, Alderson, A, and Evans, KE (2000), Do zeolites have negative Poisson’s ratios?, Adv. Mater., 12(24), 1912–1918.Google Scholar
Grima, JN (2000), New auxetic materials, Ph.D Thesis, University of Exeter, Exeter, UK.Google Scholar
Sanchez-Valle, C, Sinogeikin, SV, Lethbridge, ZAD, Walton, RI, Smith, CW, Evans, KE, and Bass, JD (2005), Brillouin scattering study on the single-crystal elastic properties of natrolite and analcime zeolites, J. Appl. Phys., 98(5), 053508.Google Scholar
Lethbridge, ZAD, Williams, JJ, Walton, RI, Smith, CW, Hooper, RM, and Evans, KE (2006), Direct, static measurement of single-crystal Young’s moduli of the zeolite natrolite: Comparison with dynamic studies and simulations, Acta Mater., 54(9), 2533–2545.Google Scholar
Smith, CW, Evans, KE, Lethbridge, ZAD, and Walton, RI (2007), An analytical model for producing negative Poisson’s ratios and its application in explaining off-axis elastic properties of the NAT-type zeolites, Acta Mater., 55(17), 5697–5707.Google Scholar
Williams, JJ, Smith, CW, Evans, KE, Lethbridge, ZAD, and Walton, RI (2007), Off-axis elastic properties and the effect of extraframework species on structural flexibility of the NAT-type zeolites: Simulations of structure and elastic properties, Chem. Mater., 19(10), 2423–2434.Google Scholar
Grima, JN, Gatt, R, Zammit, V, Williams, JJ, Alderson, A, and Walton, RI (2007), Natrolite: A zeolite with negative Poisson’s ratios, J. Appl. Phys., 101(8), 086102.Google Scholar
Grima, JN, Zammit, V, Gatt, R, Alderson, A, and Evans, KE (2007), Auxetic behaviour from rotating semi-rigid units, Phys. Status Solidi B, 224(3), 866–882.Google Scholar
Grima, JN, Gatt, R, and Chetcuti, E (2010), On the behaviour of natrolite under hydrostatic pressure, J. Non-Cryst. Solids, 356(37–40), 1881–1887.Google Scholar
Kremleva, A, Vogt, T, and Rosch, N (2013), Monovalent cation exchanged natrolites and their behaviour under pressure. A computational study, J. Phys. Chem. C, 117(37), 19020–19030.Google Scholar
Manga, ED, Blasco, H, Da-Costa, P, Drobek, M, Ayral, A, Le Clezio, E, Despaux, G, Coasne, B, and Julbe, A (2014), Effect of gas adsorption on acoustic wave propagation in MFI zeolite membrane materials: Experiment and molecular simulation, Langmuir, 30(34), 10336–10343.Google Scholar
Siddorn, M, Coudert, FX, Evans, KE, and Marmier, AA (2015), A systematic typology for negative Poisson’s ratio materials and the prediction of complete auxeticity in pure silica zeolite JST, Phys. Chem. Chem. Phys., 17(27), 17927.Google Scholar
Alderson, A and Evans, KE (2002), Molecular origin of auxetic behaviour in tetrahedral framework silicates, Phys. Rev. Lett., 89(22), 225503.Google Scholar
Alderson, A, Alderson, KL, Evans, KE, Grima, JN, Williams, MR, and Davies, PJ (2004), Molecular modelling of the deformation mechanisms acting in auxetic silica, Comput. Meth. Sci. Technol., 10(2), 117–126.Google Scholar
Alderson, A, Alderson, KL, Evans, KE, Grima, JN, and Williams, M (2005), Modelling of negative Poisson’s ratio nanomaterials: Deformation mechanisms, structure-property relationships and applications, J. Metastab. Nanocryst. Mater., 23, 55–58.Google Scholar
Gatt, R, Mizzi, L, Azzopardi, KM, and Grima, JN (2015), A force-field based analysis of the deformation in α-cristobalite, Phys. Status Solidi B, 252(7), 1479–1485.Google Scholar
Nazare, F and Alderson, A (2015), Models for the prediction of Poisson’s ratio in the α-cristobalite tetrahedral framework, Phys. Status Solidi B, 252(7), pp. 1465–1478.Google Scholar
Wojciechowski, KW (1989), Two-dimensional isotropic system with a negative Poisson ratio, Phys. Lett. A, 137(1–2), 60–64.Google Scholar
Wojciechowski, KW, Branka, AC, and Parrinello, M (1984), Monte Carlo study of the phase diagram of a two dimensional system of hard cyclic hexamers, Mol. Phys., 53(6), 1541–1545.Google Scholar
Wojciechowski, KW (1987), Constant thermodynamic tension Monte Carlo studies of elastic properties of a two-dimensional system of hard cyclic hexamers, Mol. Phys., 61(5), 1247–1258.Google Scholar
Wojciechowski, KW and Branka, AC (1989), Negative Poisson ratio in a two-dimensional “isotropic” solid, Phys. Lett. A, 40(12), 7222–7225.Google Scholar
Wojciechowski, KW and Branka, AC (1994), Auxetics: Materials and models with negative Poisson’s ratios, Mol. Phys. Rep., 6, 71.Google Scholar
Tretiakov, KV and Wojciechowski, KW (2002), Orientational phase transition between hexagonal solids in planar systems of hard cyclic pentamers and heptamers, J. Phys.: Condens. Matter, 14(6), 1261–1273.Google Scholar
Tretiakov, KV and Wojciechowski, KW (2005), Monte Carlo simulation of two-dimensional hard body systems with extreme values of the Poisson’s ratio, Phys. Status Solidi B, 242(3), 730–741.Google Scholar
Tretiakov, KV and Wojciechowski, KW (2006), Elastic properties of the degenerate crystalline phase of two-dimensional hard dimers, J. Non-Cryst. Solids, 352(40–41), 4221–4228.Google Scholar
Tretiakov, KV and Wojciechowski, KW (2007), Poisson’s ratio of simple planar “isotropic” solids in two dimensions, Phys. Status Solidi B, 244(3), 1038–1046.Google Scholar
Narojczyk, JW and Wojciechowski, KW (2007), Elastic properties of two-dimensional soft polydisperse trimers at zero temperature, Phys. Status Solidi B, 244(3), 943–954.Google Scholar
Narojczyk, JW, Alderson, A, Imre, AR, Scarpa, F, and Wojciechowski, KW (2008), Negative Poisson’s ratio behaviour in the planar model of asymmetric trimers at zero temperature, J. Non-Cryst. Solids, 354(35–39), 4242–4248.Google Scholar
Narojczyk, JW and Wojciechowski, KW (2008), Elasticity of periodic and aperiodic structures of polydisperse dimers in two dimensions at zero temperature, Phys. Status Solidi B, 245(11), 2463–2468.Google Scholar
Narojczyk, JW and Wojciechowski, KW (2010), Elastic properties of degenerate f.c.c. crystal of polydisperse soft dimers at zero temperature, J. Non-Cryst. Solids, 356(37–40), 2026–2032.Google Scholar
Narojczyk, JW, Piglowski, PM, Wojciechowski, KW, and Tretiakov, KV (2015), Elastic properties of mono and polydisperse two dimensional crystals of hard core repulsive Yukawa particles, Phys. Status Solidi B, 252(7), 1508–1513.Google Scholar
Tretiakov, KV, Piglowski, PM, Hyzorek, K, and Wojciechowski, KW (2016), Enhanced auxeticity in Yukawa systems due to introduction of nanochannels in-direction, Smart Mater. Struct., 25(5), 054007.Google Scholar
Lakes, R (1993), Advances in negative Poisson’s ratio materials, Adv. Mater., 5(4), 293–296.Google Scholar
Alderson, A (1999), A triumph of lateral thought, Chemistry & Industry, 1993(10), 384–391.Google Scholar
Yang, W, Li, ZM, Shi, W, Xie, BH, and Yang, MB (2004), Review on auxetic materials, J. Mater. Sci., 39(10), 3269–3279.Google Scholar
Alderson, A and Alderson, KL (2007), Auxetic materials, IMechE J. Aerosp. Eng., 221(4), 565–575.Google Scholar
Liu, Y and Hu, H (2010), A review on auxetic structures and polymeric materials, Scient. Res. Essays, 5(10), 1052–1063.Google Scholar
Greaves, GN, Greer, AL, Lakes, RS, and Rouxel, T (2011), Poisson’s ratio and modern materials, Nat. Mater., 10(11), 823–837.Google Scholar
Prawoto, Y (2012), Seeing auxetic materials from the mechanics point of view: A structural review on the negative Poisson’s ratio, Comput. Mater. Sci., 58, 140–153.Google Scholar
Critchley, R, Corni, I, Wharton, JA, Walsh, FC, Wood, RJK, and Stokes, KR (2013), A review of the manufacture, mechanical properties and potential applications of auxetic foams, Phys. Status Solidi B, 250(10), 1963–1982.Google Scholar
Saxena, KK, Das, R, and Calius, EP (2016), Three decades of auxetics research − materials with negative Poisson’s ratio: A review, Adv. Eng. Mater., 18(11), 1847–1870.Google Scholar
Lakes, RS (2017), Negative-Poisson’s-ratio materials: Auxetic solids, Ann. Rev. Mater. Res., 47, 63–81.Google Scholar
Lim, TC (2017), Analogies across auxetic models based on deformation mechanism, Phys. Status Solidi RRL, 11(6), 1600440.Google Scholar
Kolken, HMA and Zadpoor, AA (2017), Auxetic mechanical metamaterials, RSC Adv., 7(9), 5111–5129.Google Scholar
Ren, X, Das, R, Tran, P, Ngo, T, and Xie, YM (2018), Auxetic metamaterials and structures: A review, Smart Mater. Struct., 27(2), 023001.Google Scholar
Darja, R, Tatjana, R, and Alenka, PC (2013), Auxetic textiles, Acta Chim. Slov., 60(4), 715–723.Google Scholar
Jiang, JW, Kim, SY, and Park, HS (2016), Auxetic nanomaterials: Recent progress and future development, Appl. Phys. Rev., 3, 041101.Google Scholar
Park, HS and Kim, SY (2017), A perspective on auxetic nanomaterials, Nano Converg., 4, 10.Google Scholar
Duncan, O, Shepherd, T, Moroney, C, Foster, L, Venkatraman, PD, Winwood, K, Allen, T, and Alderson, A (2018), Review of auxetic materials for sports applications: Expanding options in comfort and protection, Appl. Sci., 8(6), 941.Google Scholar
Kwietniewski, M and Miedzińska, D (2019), Review of elastomeric materials for application to composites reinforced by auxetics fabrics, Proc. Struct. Integrity, 17, 154–161.Google Scholar
Wu, W, Hu, W, Qian, G, Liao, H, Xu, X, and Berto, F (2019), Mechanical design and multifunctional applications of chiral mechanical metamaterials: A review, Mater. Des., 180, 107950.Google Scholar
Zhang, J, Lu, G, and You, Z (2020), Large deformation and energy absorption of additively manufactured auxetic materials and structure: A review, Compos. Part B: Eng., 201, 108340.Google Scholar
Grether, GF, Kolluru, GR, and Nersissian, K (2004), Individual colour patches as multicomponent signals, Biol. Rev. (Camb. Philos. Soc.), 79(3), 583–610.Google Scholar
Saenko, SV, Teyssier, J, van der Marel, D, and Milinkovitch, MC (2013), Precise colocalization of interacting structural and pigmentary elements generates extensive color pattern variation in Phelsuma lizards, BMC Biol., 11, 105.Google Scholar
Teyssier, J, Saenko, SV, Marel, van der, and Milinkovitch, MC (2015), Photonic crystals cause active colour change in chameleons, Nat. Commun., 6, 6368.Google Scholar
Hedayati, MK and Elbahri, M (2017), Review of metasurface plasmonic structural color, Plasmonics, 12(5), 1463–1479.Google Scholar
Galinski, H, Favraud, G, Dong, H, Gongora, JST, Favaro, G, Döbeli, M, Spolenak, R, Fratalocchi, A, and Capasso, F (2017), Scalable, ultra-resistant structural colors based on network metamaterials, Light: Sci. Appl., 6, e16233.Google Scholar
Huang, L, Duan, Y, Dai, X, Zeng, Y, Ma, G, Liu, Y, Gao, S, and Zhang, W (2019), Bioinspired metamaterials: Multibands electromagnetic wave adaptability and hydrophobic characteristics, Small 15(40), 1902730.Google Scholar
Lee, N, Kim, T, Lim, JS, Chang, I, and Cho, HH (2019), Metamaterial-selective emitter for maximizing infrared camouflage performance with energy dissipation, Appl. Mater. Interf., 11(23), 21250–21257.Google Scholar
Rafsanjani, A and Pasini, D (2016), Multistable compliant auxetic metamaterials inspired by geometric patterns in Islamic arts, Bull. Am. Phys. Soc., 61, K40.00008.Google Scholar
Rafsanjani, A and Pasini, D (2016), Bistable auxetic mechanical metamaterials inspired by ancient geometric motifs, Extreme Mech. Lett., 9, 291–296.Google Scholar
Ravirala, N, Alderson, A, and Alderson, KL (2007), Interlocking hexagonal model for auxetic behaviour, J. Mater. Sci., 42(17), 7433–7445, 2007.Google Scholar
Lim, TC (2021), A perfect 2D auxetic sliding mechanism based on an Islamic geometric pattern, Eng. Res. Express, 3(1), 015025.Google Scholar
Larsen, UD, Sigmund, O, and Bouwstra, S (1997), Design and fabrication of compliant mechanisms and material structures with negative Poisson’s ratio, J. Microelectromech. Syst., 6(2), 99–106.Google Scholar
Li, Y, Chen, Y, Li, T, Cao, S, and Wang, L (2018), Hoberman-sphere-inspired lattice metamaterials with tunable negative thermal expansion, Compos. Struct., 189, 586–597.Google Scholar
Lim, TC (2020), Metacomposite structure with sign-changing coefficients of hygrothermal expansions inspired by Islamic motif, Compos. Struct., 251, 112660.Google Scholar
Cabras, L, Brun, M, and Misseroni, D (2019), Micro-structured medium with large isotropic negative thermal expansion, Proc. Royal Soc A, 475(2232), 20190463.Google Scholar
Lim, TC (2021), An auxetic system based on interconnected Y-elements inspired by Islamic geometric patterns, Symmetry, 13(5), 865.Google Scholar
Lim, TC (2021), Aspect ratio and size effects of a metacomposite with interconnected Y-elements, J. Phys.: Conf. Ser., 2047, 012029.Google Scholar
Lakes, R (1996), Cellular solid structures with unbounded thermal expansion, J. Mater. Sci. Lett., 15(6), 475–477.Google Scholar
Lakes, R (2007), Cellular solids with tunable positive or negative thermal expansion of unbounded magnitude, Appl. Phys. Lett., 90(22), 221905.Google Scholar
Lim, TC (2020), Composite metamaterial square grids with sign-flipping expansion coefficients leading to a type of Islamic design, SN Appl. Sci., 2(5), 918.Google Scholar
Lim, TC (2021), Metamaterial honeycomb with sign-toggling expansion coefficients that manifests an Islamic mosaic pattern at the Alhambra Palace, Adv. Compos. Hybrid Mater., 4(4), 966–978.Google Scholar
Lim, TC (2022), Metamaterial with sign-toggling thermal expansivity inspired by Islamic motifs in Spain, J. Sci.: Adv. Mater. Dev., 7(1), 100401.Google Scholar
Hashemi, MRM, Yang, SH, Wang, T, Sepúlveda, N, and Jarrahi, M (2016), Electronically-controlled beam-steering through vanadium dioxide metasurfaces, Scient. Rep. 6, 35439.Google Scholar
Wang, GD, Liu, MH, Hu, XW, Kong, LH, Cheng, LL, and Chen, ZQ (2013), Multi-band microwave metamaterial absorber based on coplanar Jerusalem crosses, Chin. Phys. B, 23(1), 017802.Google Scholar
Arezoomand, AS, Zarrabi, FB, Heydari, S, and Gandji, NP (2015), Independent polarization and multi-band THz absorber base on Jerusalem cross, Optics Commun., 352, 121–126.Google Scholar
Mi, S and Lee, HY (2016), Design of a compact patch antenna loading periodic Jerusalem crosses, Prog. Electromag. Res. M, 47, 151–159.Google Scholar
Naser-Moghadasi, M, Nia, AZ, Toolabi, M, and Heydari, S (2017), Microwave metamaterial absorber based on Jerusalem cross with meandered load for bandwidth enhancement, Optik, 140, 515–522.Google Scholar
Silva Filho, HVH, Silva, CPN, de Oliveira, MRT, de Oliveira, EMF, de Melo, MT, de Sousa, TR, and Gomes Neto, A (2017), Multiband FSS with fractal characteristic based on Jerusalem cross geometry, J. Microwaves Optoelectron. Electromag. Appl., 16(4), 932–941.Google Scholar
Jafari, FS, Naderi, M, Hatami, A, and Zarrabi, FB (2019), Microwave Jerusalem cross absorber by metamaterial split ring resonator load to obtain polarization independence with triple band application, AEU – Int. J. Electron. Commun., 101(5), 138–144.Google Scholar
Kamonsin, W, Krachodnok, P, Chomtong, P, and Akkaraekthalin, P (2020), Dual-band metamaterial based on Jerusalem cross structure with interdigital technique for LTE and WLAN systems, IEEE Access, 8, 21565–21572.Google Scholar
Tang, Y, He, L, Liu, A, Xiong, C, and Xu, H (2020), Optically transparent metamaterial absorber based on Jerusalem cross structure at S-band frequencies, Modern Phys. Lett. B, 34(16), 2050175.Google Scholar
Hannan, S, Islam, MT, Almutairi, AF, and Faruque, MRI (2020), Wide bandwidth angle- and polarization-insensitive symmetric metamaterial absorber for X and Ku band applications, Scient. Rep., 10, 10338.Google Scholar
Liu, Q, Liang, D, Wang, X, Han, T, Lu, H, and Xie, J (2021), Jerusalem cross geometry magnetic substrate absorbers for low-frequency broadband applications, AIP Adv., 11(3), 035037.Google Scholar
Lee, SC, Kang, JH, Park, QH, Krishna, S, and Brueck, SRJ (2016), Oscillatory penetration of near-fields in plasmonic excitation at metal-dielectric interfaces, Scient. Rep., 6, 24400.Google Scholar
Lim, TC (2019), An anisotropic auxetic 2D metamaterial based on sliding microstructural mechanism, Mater., 12(3), 429.Google Scholar
Cabras, L and Brun, M (2014), Auxetic two-dimensional lattices with Poisson’s ratio arbitrarily close to –1, Proc. Royal. Soc. A, 470(2172), 20140538.Google Scholar
Lim, TC (2021), An auxetic metamaterial with tunable positive to negative hygrothermal expansion by means of counter‐rotating crosses, Phys. Status Solidi B, 258(8), 2100137.Google Scholar
Zhu, WM, Liu, AQ, Bourouina, T, Tsai, DP, Teng, JH, Zhang, XH, Lo, GQ, Kwong, DL, and Zheludev, NI (2012), Microelectromechanical Maltese-cross metamaterial with tunable terahertz anisotropy, Nat. Commun., 3, 1274.Google Scholar
Lim, TC (2021), Adjustable positive and negative hygrothermal expansion metamaterial inspired by the Maltese cross, Royal Soc. Open Sci., 8(8), 210593.Google Scholar
Evans, KE and Alderson, A (2000), Auxetic materials: Functional materials and structures from lateral thinking!, Adv. Mater., 12(9), 617–628.Google Scholar
Cheng, HC, Scarpa, F, Panzera, TH, Farrow, I, and Peng, HX (2019), Shear stiffness and energy absorption of auxetic open cell foams as sandwich cores, Phys. Status Solidi B, 256(1), 1800411.Google Scholar
Bliven, E, Rouhier, A, Tsai, S, Wilinger, R, Bourdet, N, Deck, C, Madey, SM, and Bottlang, M (2019), Evaluation of a novel bicycle helmet concept in oblique impact testing, Accident Anal. Prevent., 124, 58–65.Google Scholar
Smith, CW, Grima, JN, and Evans, KE (2000), A novel mechanism for generating auxetic behaviour in reticulated foams: Missing rib foam model, Acta Mater., 48(17), 4349–4356.Google Scholar
Zhong, R, Fu, M, Yin, Q, Xu, O, and Hu, L (2019), Special characteristics of tetrachiral honeycombs under large deformation, Int. J. Solids Struct., 169, 166–176.Google Scholar
Alderson, A, Alderson, KL, Attard, D, Evans, KE, Gatt, R, Grima, JN, Miler, W, Ravirala, N, Smith, CW, and Zied, K (2010), Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading, Compos. Sci. Technol., 70(7), 1042–1048.Google Scholar
Caruana-Gauci, R, Degabriele, EP, Attard, D, and Grima, JN (2018), Auxetic metamaterial inspired from wine-racks, J. Mater. Sci., 53(7), 5079–5091.Google Scholar
Gatt, R, Mizzi, L, Azzopardi, JI, Azzopardi, KM, Attard, D, Casha, A, Briffa, J, and Grima, JN (2015), Hierarchical auxetic mechanical metamaterials, Scient. Rep., 5, 8395.Google Scholar
Meza, LR, Zelhofer, AJ, Clarke, N, Mateos, AJ, Kochmann, DM, and Greer, JR (2015), Resilient 3D hierarchical architected metamaterials, Proc. Nat. Acad. Sci., 112(37), 11502–11507.Google Scholar
Mousanezhad, D, Babaee, S, Ebrahimi, H, Ghosh, R, Hamouda, AS, Bertoldi, K, and Vaziri, A (2016), Hierarchical honeycomb auxetic metamaterials, Scient. Rep., 5, 18306.Google Scholar
Chen, Y, Jia, Z, and Wang, L (2016), Hierarchical honeycomb lattice metamaterials with improved thermal resistance and mechanical properties, Compos. Struct., 152, 395–402.Google Scholar
Grima-Cornish, JN, Grima, JN, and Evans, KE (2017), On the structural and mechanical properties of poly(phenylacetylene) truss-like hexagonal hierarchical nanonetworks, Phys. Status Solidi B, 254(12), 1700190.Google Scholar
Billon, K, Zampetakis, I, Scarpa, F, Ouisse, M, Sadoulet-Reboul, E, Collet, M, Perriman, A, and Hetherington, A (2017), Mechanics and band gaps in hierarchical auxetic rectangular perforated composite metamaterials, Compos. Struct., 160, 1042–1050.Google Scholar
Yang, H, Wang, B, and Ma, L (2019), Designing hierarchical metamaterials by topology analysis with tailored Poisson’s ratio and Young’s modulus, Compos. Struct., 214, 359–378.Google Scholar
Zhang, W, Zhao, S, Sun, R, Scarpa, F, and Wang, J (2019), In-plane mechanical behavior of a new star-re-entrant hierarchical metamaterial, Polym., 11(7), 1132.Google Scholar
Kochmann, DM, Hopkins, JB, and Valdevit, L (2019), Multiscale modeling and optimization of the mechanics of hierarchical metamaterials, MRS Bull., 44(10), 773–781.Google Scholar
Zhang, H, Wu, J, Fang, D, and Zhang, Y (2021), Hierarchical mechanical metamaterials built with scalable tristable elements for ternary logic operation and amplitude modulation, Sci. Adv., 7(9), eabf1966.Google Scholar
Guo, X, Ni, X, Li, J, Zhang, H, Zhang, F, Yu, H, Wu, J, Bai, Y, Lei, H, Huang, Y, Rogers, JA, and Zhang, H (2021), Designing mechanical metamaterials with kirigami inspired, hierarchical constructions for giant positive and negative thermal expansion, Adv. Mater., 33(3), 2004919.Google Scholar
Dudek, KK, Gatt, R, Dudel, MR, and Grima, JN (2021), Controllable hierarchical mechanical metamaterials guided by the hinge design, Materials, 14(4), 758.Google Scholar
Morvaridi, M, Carta, G, Bosia, F, Gliozzi, AS, Pugno, NM, Misseroni, D, and Brun, M (2021), Hierarchical auxetic and isotropic porous medium with extremely negative Poisson’s ratio, Extreme Mech. Lett., 48, 101405.Google Scholar
Wu, H, Cheng, Y, Liu, W, He, R, Zhou, M, Wu, S, Song, X, and Chen, Y (2016), Effect of the particle size and the debinding process on the density of alumina ceramics fabricated by 3D printing based on stereolithography, Ceram. Int., 42(15), 17290–17294.Google Scholar
Domènech, B, Tan, ATL, Jelitto, H, Berodt, EZ, Blankenburg, M, Focke, O, Cann Tasan CC, J, Ciacchi, LC, Müller, M, Furlan, KP, Hart, AJ, and Schneider, GA (2020), Strong macroscale supercrystalline structures by 3D printing combined with self-assembly of ceramic functionalized nanoparticles, Adv. Eng. Mater., 22 (7), 2000352.Google Scholar
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