References
- H.H. Huang and C.T. Sun, Locally resonant acoustic metamaterials with 2D anisotropic effective mass density. Philos. Mag. 91 (2011), pp. 981–996.
- M. Dunn and M. Wheel, Size effect anomalies in the behavior of loaded 3D mechanical metamaterials. Philos. Mag. 100 (2020), pp. 139–156.
- A.J.C.B. Saint-Venant, Résumé des leçons sur l’application de la mécanique à l’établissement des constructions et des machines, premiere section, E. Thunot et Cie, Paris, 1848.
- W. Voigt, Lehrbuch der Kristallphysik, Teubner, Berlin, 1910.
- D. Berlincourt and H. Jaffe, Elastic and piezoelectric coefficients of single-crystal barium titanate. Phys. Rev. 111 (1958), pp. 143–148.
- D.J. Gunton and G.A. Saunders, The Young’s modulus and Poisson’s ratio of arsenic, antimony and bismuth. J. Mater. Sci. 7 (1972), pp. 1061–1068.
- Y. Li, The anisotropic behavior of Poisson’s ratio, Young’s modulus, and shear modulus in hexagonal materials. Phys. Status Solidi 38 (1976), pp. 171–175.
- F. Milstein and K. Huang, Existence of a negative Poisson ratio in FCC crystals. Phys. Rev. B 19 (1979), pp. 2030–2033.
- E. Kittinger, J. Tichy, and E. Bertagnolli, Example of a negative effective Poisson’s ratio. Phys. Rev. Lett. 47 (1981), pp. 712–714.
- R. Lakes, Foam structures with a negative Poisson’s ratio. Science 235 (1987), pp. 1038–1040.
- R. Lakes, Negative Poisson’s ratio materials. Science 238 (1987), p. 551.
- K.E. Evans, M.A. Nkansah, I.J. Hutchinson, and S.C. Rogers, Molecular network design. Nature 353 (1991), p. 124.
- K.W. Wojciechowski, Constant thermodynamic tension Monte-Carlo studies of elastic properties of a two-dimensional system of hard cyclic hexamers. Mol. Phys. 61 (1987), pp. 1247–1258.
- A. Yeganeh-Haeri, D.J. Weidner, and J.B. Parise, Elasticity of α-cristobalite: a silicon dioxide with a negative Poisson’s ratio. Science 257 (1992), pp. 650–652.
- A. Alderson and K.E. Evans, Microstructural modelling of auxetic microporous polymers. J. Mater. Sci. 30 (1995), pp. 3319–3332.
- R.H. Baughman, J.M. Shacklette, A.A. Zakhidov, and S. Stafström, Negative Poisson’s ratios as a common feature of cubic metals. Nature 392 (1998), pp. 362–365.
- F. Scarpa, P. Panayiotou, and G. Tomlinson, Numerical and experimental uniaxial loading on in-plane auxetic honeycombs. J. Strain Anal. Eng. Des. 35 (2000), pp. 383–388.
- J.N. Grima and K.E. Evans, Auxetic behaviour from rotating squares. J. Mater. Sci. Lett. 19 (2000), pp. 1563–1565.
- Y. Ishibashi and M. Iwata, A microscopic model of a negative Poisson’s ratio in some crystals. J. Phys. Soc. Jpn. 69 (2000), pp. 2702–2703.
- J.B. Choi and R.S. Lakes, Design of a fastener based on negative Poisson's ratio foam. Cell. Polym. 10 (1991), pp. 205–212.
- B.D. Caddock and K.E. Evans, Negative Poisson ratios and strain-dependent mechanical properties in arterial prostheses. Biomater 16 (1995), pp. 1109–1115.
- N. Karnessis and G. Burriesci, Uniaxial and buckling mechanical response of auxetic cellular tubes, Smart Mater. Struct 22 (2013), p. 084008.
- E.O. Martz, R.S. Lakes, V.K. Goel, and J.B. Park, Design of an artificial intervertebral disc exhibiting a negative Poisson's ratio. Cell. Polym. 24 (2005), pp. 127–138.
- W.J.S. Dolla, B.A. Fricke, and B.R. Becker, Structural and drug diffusion models of conventional and auxetic drug-eluting stents. J. Med. Devices 1 (2007), pp. 47–55.
- F. Scarpa, Auxetic materials for bioprostheses. IEEE Signal Process. Mag. 25 (2008), pp. 125–126.
- R.S. Lakes and A. Lowe, Negative Poisson's ratio foam as seat cushion material. Cell. Polym. 19 (2000), pp. 157–167.
- Y.C. Wang and R.S. Lakes, Analytical parametric analysis of the contact problem of human buttocks and negative Poisson’s ratio foam cushions. Int. J. Solids Struct. 39 (2002), pp. 4825–4838.
- A. Alderson, J. Rasburn, S. Ameer-Bag, P.G. Mullarkey, W. Perrie, and K.E. Evans, An auxetic filter: A tuneable filter displaying enhanced size selectivity or defouling properties. Indust. Eng. Chem. Res. 39 (2000), pp. 654–655.
- A. Alderson, P.J. Davies, K.E. Evans, K.L. Alderson, and J.N. Grima, Modelling of the mechanical and mass transport properties of auxetic molecular sieves: An idealised inorganic (zeolitic) host-guest system. Mol. Simul. 31 (2005), pp. 889–896.
- A. Alderson, P.J. Davies, M.R. Williams, K.E. Evans, K.L. Alderson, and J.N. Grima, Modelling of the mechanical and mass transport properties of auxetic molecular sieves: An idealised organic (polymeric honeycomb) host-guest system. Mol. Simul. 31 (2005), pp. 897–905.
- T.C. Lim and R.U. Acharya, Performance evaluation of auxetic molecular sieves with re-entrant structures. J. Biomed. Nanotechnol. 6 (2010), pp. 718–724.
- A. Alderson and K.L. Alderson, Expanding materials and applications: Exploiting auxetic textiles. Tech. Text. Int. 14 (2005), pp. 29–34.
- Z. Ge, H. Hu, and Y. Liu, A finite element analysis of a 3D auxetic textile structure for composite reinforcement. Smart Mater. Struct. 22 (2013), p. 084005.
- K.O. Park, J.B. Choi, S.J. Lee, H.H. Choi, and J.K. Kim, Polyurethane foam with a negative Poisson's ratio for diabetic shoes. Key Eng. Mater. 288-289 (2005), pp. 677–680.
- L.A.S. Mercieca, C. Formosa, J.N. Grima, N. Chockalingam, R. Gatt, and A. Gatt, On the use of auxetics in footwear: Investigating the effect of padding and padding material on forefoot pressure in high heels. Phys. Status Solidi B 254 (2017), p. 1700528.
- F. Scarpa, J. Giacomin, Y. Zhang, and P. Pastorino, Mechanical performance of auxetic polyurethane foam for antivibration glove applications. Cell. Polym. 24 (2005), pp. 253–268.
- B. Henderson, J.P.M. Whitty, P. Myler, and C. Chirwa, Crash performance of cellular foams with reduced relative density part 2: Rib deletion. Int. J. Crashworthiness 12 (2007), pp. 689–698.
- K.O. Park, J.B. Choi, J.C. Park, D.J. Park, and J.K. Kim, An improvement in shock absorbing behavior of polyurethane foam with a negative Poisson effect. Key Eng. Mater. 342-343 (2007), pp. 845–848.
- M. Bianchi and F. Scarpa, Vibration transmissibility and damping behaviour for auxetic and conventional foams under linear and nonlinear regimes. Smart Mater. Struct. 22 (2013), p. 084010.
- Y. Ma, F. Scarpa, D. Zhang, B. Zhu, L. Chen, and J. Hong, A nonlinear auxetic structural vibration damper with metal rubber particles. Smart Mater. Struct. 22 (2013), p. 084012.
- F. Agnese, C. Remillat, F. Scarpa, and C. Payne, Composite chiral shear vibration damper. Compos. Struct. 132 (2015), pp. 215–225.
- A. Alderson and K.L. Alderson, Auxetic materials. J. Aerosp. Eng. 221 (2007), pp. 565–575.
- A. Airoldi, P. Bettini, P. Panichelli, M.F. Oktem, and G. Sala, Chiral topologies for composite morphing structures–Part I: Development of a chiral rib for deformable airfoils. Phys. Status Solidi B 252 (2015), pp. 1435–1445.
- T.C. Lim, In-plane stiffness of semiauxetic laminates. J. Eng. Mech. 136 (2010), pp. 176–1180.
- L. Boldrin, S. Hummel, F. Scarpa, D.D. Maio, C. Lira, M. Ruzzene, C.D.L. Remillat, T.C. Lim, R. Rajasekaran, and S. Patsias, Dynamic behaviour of auxetic gradient composite hexagonal honeycombs. Compos. Struct. 149 (2016), pp. 114–124.
- T. Allen, N. Martinello, D. Zampieri, T. Hewage, T. Senior, L. Foster, and A. Alderson, Auxetic foams for sport safety applications. Procedia Eng. 112 (2015), pp. 104–109.
- T. Allen, O. Duncan, O. Foster, T. Senior, D. Zampieri, V. Edeh, and A. Alderson, Auxetic foam for snow-sport safety devices, in Snow Sports Trauma and Safety, I.S. Scher, R.M. Greenwald, and N. Petrone, eds., Springer Nature, Cham, Switzerland, 2017, pp. 145–159.
- G.N. Greaves, A.L. Greer, R.S. Lakes, and T. Rouxel, Poisson's ratio and modern materials. Nat. Mater. 10 (2011), pp. 823–837.
- R.S. Lakes, Negative-Poisson's-ratio materials: Auxetic solids. Ann. Rev. Mater. Res. 47 (2017), pp. 63–81.
- T.C. Lim, Analogies across auxetic models based on deformation mechanism. Phys. Status Solidi RRL 11 (2017), p. 1600440.
- H.M.A. Kolken and A.A. Zadpoor, Auxetic mechanical metamaterials. RSC Adv. 7 (2017), pp. 5111–5129.
- X. Ren, R. Das, P. Tran, T. Ngo, and Y.M. Xie, Auxetic metamaterials and structures: a review. Smart Mater. Struct 27 (2018), p. 023001.
- E. Barchiesi, M. Spagnuolo, and L. Placidi, Mechanical metamaterials: A state of the art. Math. Mech. Solids 24 (2019), pp. 212–234.
- W. Wu, W. Hu, G. Qian, H. Liao, X. Xu, and F. Berto, Mechanical design and multifunctional applications of chiral mechanical metamaterials: A review. Mater. Des. 180 (2019), p. 107950.
- S. Shukla and B.K. Behera, Auxetic fibrous structures and their composites: A review. Compos. Struct. 290 (2022), p. 115530.
- D. Tahir, M. Zhang, and H. Hu, Auxetic materials for personal protection: A review. Phys. Status Solidi B 259 (2022), p. 2200324.
- U. Veerabagu, H. Palza, and F. Quero, Review: Auxetic polymer-based mechanical metamaterials for biomedical application. ACS Biomater. Sci. Eng. 8 (2002), pp. 2798–2824.
- T.C. Lim, Auxetic Materials and Structures, Springer Nature, Singapore, 2015.
- H. Hu, M. Zhang, and Y. Liu, Auxetic Textiles, Elsevier, Cambridge, 2019.
- R. Lakes, Composites and Metamaterials, World Scientific, Singapore, 2020.
- T.C. Lim, Mechanics of Metamaterials with Negative Parameters, Springer Nature, Singapore, 2020.
- J.N. Grima, A. Alderson, and K.E. Evans, Negative Poisson’s ratio from rotating rectangles. Comput. Meth. Sci. Technol. 10 (2004), pp. 137–145.
- J.N. Grima, R. Gatt, A. Alderson, and K.E. Evans, On the auxetic properties of ‘rotating rectangles’ with different connectivity. J. Phys. Soc. Jpn. 74 (2005), pp. 2866–2286.
- J.N. Grima, E. Manicaro, and D. Attard, Auxetic behaviour from connected different-sized squares and rectangles. Proc. Royal Soc. A 467 (2011), pp. 439–458.
- D. Attard and J.N. Grima, Auxetic behaviour from rotating rhombi. Phys. Status Solidi B 245 (2008), pp. 2395–2404.
- D. Attard, E. Manicaro, and J.N. Grima, On rotating parallelograms and their potential for exhibiting auxetic behavior. Phys. Status Solidi B 246 (2009), pp. 2033–2044.
- T.C. Lim, A metamaterial with sign-programmable thermal expansivity and Poisson’s ratio constructed from a hybrid of rotating and non-rotating rigid units. Int. J. Solids Struct. 284 (2023), p. 112510.
- J.N. Grima and K.E. Evans, Auxetic behaviour from rotating triangles. J. Mater. Sci. 41 (2006), pp. 3193–3196.
- J.N. Grima, E. Chetcuti, E. Manicaro, D. Attard, M. Camilleri, R. Gatt, and K.E. Evans, On the auxetic properties of generic rotating rigid triangles. Proc. Royal Soc. A 468 (2012), pp. 810–830.
- T.C. Lim, An auxetic metamaterial based on rotating and nonrotating rigid units inspired by an Aztec geometric pattern. Phys. Status Solidi B 259 (2022), p. 2200385.
- T.C. Lim, An anisotropic negative thermal expansion metamaterial with sign-toggling and sign-programmable Poisson’s ratio. Oxford Open Mater. Sci. 2 (2022), p. itac007.
- T.C. Lim, Auxetic properties of a tangram-inspired metamaterial. Eng. Res. Express 5 (2023), p. 015063.
- T.C. Lim, A metamaterial with negative thermal expansivity and programmable Poisson's ratio based on rotating triangles and quivering rhombi. Eur. J. Mech.-A/Solids 100 (2023), p. 104986.
- T.C. Lim, Auxetic and non-auxetic metamaterial model from interconnected rotating parallelograms and triangles. Phys. Status Solidi B 261 (2024), p. 2300413.
- T.C. Lim, A Partially Auxetic Metamaterial Inspired by the Maltese Cross, Cambridge University Press, Cambridge, UK, 2022.
- T.C. Lim, Metamaterials with Poisson's ratio discontinuity by means of fragmentation–reconstitution rotating units. Proc. Royal Soc. A 479 (2023), p. 20230442.