We investigate geometric characteristics of a specific planar periodic framework with three degrees of freedom. While several avatars of this structural design have been considered in materials science under the name of chiral or missing rib models, all previous studies have addressed only local properties and limited deployment scenarios. We describe the global configuration space of the framework and emphasize the geometric underpinnings of auxetic deformations. Analogous structures may be considered in arbitrary dimension.
WojciechowskiKW.Two-dimensional isotropic system with a negative Poisson ratio. Phys Lett A1989; 137(1,2): 60–64.
2.
LakesR.Deformation mechanisms in negative Poisson’s ratio materials: Structural aspects. J Mater Sci1991; 26: 2287.
3.
PrallDLakesRS.Properties of a chiral honeycomb with a Poisson’s ratio of . Int J Mech Sci1997; 39: 305–314.
4.
SigmundOTorquatoSAskayIA.On the design of 1-3 piezocomposites using topology optimization. J Mater Res1998; 13: 1038–1048.
5.
GasparNRenXJSmithCW, et al. Novel honeycombs with auxetic behaviour. Acta Mater2005; 53: 2439–2445.
6.
AldersonAAldersonKLAttardD, et al. Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading. Compos Sci Technol2010; 70: 1042–1048.
7.
RossiterJTakashimaKScarpaF, et al. Shape memory polymer hexachiral auxetic structures with tunable stiffness. Smart Mater Struct2014; 23: 045007.
8.
FredericksonGN.Hinged dissections: Swinging & twisting. Cambridge: Cambridge University Press, 2002.
9.
MitschkeHSchwerdtfegerJSchuryF, et al. Finding auxetic frameworks in periodic tessellations. Adv Mater2011; 23: 2669–2674.
10.
MitschkeHRobinsVMeckeK, et al. Finite auxetic deformations of plane tessellations. Proc R Soc London, Ser A2013; 469: 20120465.
11.
MitschkeHSchuryFMeckeK, et al. Geometry: The leading parameter for the Poisson’s ratio of bending-dominated cellular solids. Int J Solids Struct2016; 100–101: 1–10.
12.
MousanezhadDHaghpanahBGhoshR, et al. Elastic properties of chiral, anti-chiral, and hierarchical honeycombs: A simple energy-based approach. Theor Appl Mech Lett2016; 6: 81–96.
13.
JiangYLiY.3D printed chiral cellular solids with amplified auxetic effects due to elevated internal rotation. Adv Eng Mater2017; 19: 1600609.
14.
IdezakEStrekT.Minimization of Poisson’s ratio in anti-tetra-chiral two-phase structure. IOP Conf Ser: Mater Sci Eng2017; 248: 012006.
15.
LimTC.Analogies across auxetic models based on deformation mechanism. Phys Status Solidi RRL2017; 11(6): 1600440.
16.
BacigalupoAGneccoGLepidiM, et al. Optimal design of low-frequency band gaps in anti-tetrachiral lattice meta-materials. Composites, Part B2017; 115: 341–359.
17.
BarchiesiESpagnuoloMPlacidiL.Mechanical metamaterials: A state of the art. Math Mech Solids2019; 24(1): 212–234.
18.
WuWQiDLiaoH, et al. Deformation mechanism of innovative 3D chiral metamaterials. Sci Rep2018; 8: 12575.
19.
WuWHuWQianG, et al. Mechanical design and multifunctional applications of chiral mechanical metamaterials: A review. Mater Des2019; 180: 107950.
20.
FarrugiaPSGattRLonardelliEZ, et al. Different deformation mechanisms leading to auxetic behavior exhibited by missing rib square grid structures. Phys Status Solidi B2019; 256: 1800186.
21.
BorceaCSStreinuI.Periodic frameworks and flexibility. Proc R Soc London, Ser A2010; 466: 2633–2649.
22.
BorceaCSStreinuI.Liftings and stresses for planar periodic frameworks. Discrete Comput Geom2015; 53: 747–782.
23.
BorceaCSStreinuI.Geometric auxetics. Proc R Soc London, Ser A2015; 471: 20150033.
GoodwinALKeenDATuckerMG, et al. Argentophilicity-dependent colossal thermal expansion in extended Prussian blue analogues. J Am Chem Soc2008; 130: 9660–9661.
