Abstract
This chapter views 2D auxetic models, including 3D deformation models with 2D auxetic behavior, from mechanism perspective instead of geometrical perspective. On this basis, auxetic models across different geometrical groups can be regrouped into clusters that exhibit analogy in deformation mechanism. Factors that are taken into consideration include the identification of corresponding rotation and non-rotation units, as well as linkages/joints between rotation and non-rotation units and non-linkages/non-joints across various auxetic models. As a result, five clusters of auxetic models have been identified, in which auxetic models within each cluster are analogous to each other. The identified clusters are those that exhibit: (1) double periodicity in the rotation direction of their rotating units, (2) synchronized rotation direction of their rotation units, (3) single periodicity in the rotation direction of their rotating units, (4) random rotation of their rotation units, and (5) non-rotation of units. Results from this analogy identification place auxetic models in a systematic representation and will enrich the future development of auxetic models, particularly, those that do not fall within these five clusters.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alderson A (1999) A triumph of lateral thought. Chem Ind 10:384–391
Alderson A, Alderson KL, Chirima G, Ravirala N, Zied KM (2010) The in-plane linear elastic constants and out-of-plane bending of 3-coordinated ligament and cylinder-ligament honeycombs. Compos Sci Technol 70(7):1034–1041
Bertoldi K, Reis PM, Wilshaw S, Mullin T (2010) Negative Poisson’s ratio behavior induced by an elastic instability. Adv Mater 22(3):361–366
Chen YJ, Scarpa F, Liu YJ, Leng JS (2013) Elasticity of antitetrachiral anisotropic lattices. Int J Solids Struct 50(6):996–1004
Gaspar N, Ren XJ, Smith CW, Grima JN, Evans KE (2005) Novel honeycombs with auxetic behavior. Acta Mater 53(8):2439–2445
Gibson LJ, Ashby MF (1988) Cellular solids: structure & properties. Pergamon Press, Oxford
Grima JN, Evans KE (2000) Auxetic behavior from rotating squares. J Mater Sci Lett 19(17):1563–1565
Grima JN, Williams JJ, Evans KE (2005a) Networked calix[4]arene polymers with unusual mechanical properties. Chem Commun 32:4065–4067
Grima JN, Gatt R, Alderson A, Evans KE (2005b) On the potential of connected stars as auxetic systems. Mol Simul 31(13):925–935
Grima JN, Zammit V, Gatt R, Alderson A, Evans KE (2007) Auxetic behavior from rotating semi-rigid units. Phys Status Solidi B 244(3):866–882
Grima JN, Gatt R, Farrugia PS (2008) On the properties of auxetic meta-tetrachiral structures. Phys Status Solidi B 245(3):511–520
Grima JN, Winczewski S, Mizzi L, Grech MC, Cauchi R, Gatt R, Attard D, Wojciechowski KW, Rybicki J (2015) Tailoring graphene to achieve negative Poisson’s ratio properties. Adv Mater 27(8):1455–1459
Haghpanah B, Papadopoulos J, Mousanezhad D, Nayeb-Hashemi H, Vaziri A (2014) Buckling of regular, chiral and hierarchical honeycombs under a general macroscopic stress state. Proc Royal Soc A 470(2167):20130856
He CB, Liu PW, Griffin AC (1998) Toward negative Poisson ratio polymers through molecular design. Macromol 31(9):3145–3147
He CB, Liu PW, McMullan PJ, Griffin AC (2005) Toward molecular auxetics: main chain liquid crystalline polymers consisting of laterally attached para-quaterphenyls. Phys Status Solidi B 242(3):576–584
Hewage TAM, Alderson KL, Alderson A, Scarpa F (2016) Double-negative mechanical metamaterials displaying simultaneous negative stiffness and negative Poisson’s ratio properties. Adv Mater 28(46):10323–10332
Javid F, Smith-Roberge E, Innes MC, Shanian A, Weaver JC, Bertoldi K (2015) Dimpled elastic sheets: a new class of non-porous negative Poisson’s ratio materials. Scient Rep 5:18373
Jiang Y, Li Y (2017) 3D printed chiral cellular solids with amplified auxetic effects due to elevated internal rotation. Adv Eng Mater 19(2):1600609
Larsen UD, Sigmund O, Bouwstra S (1997) Design and fabrication of compliant mechanisms and material structures with negative Poisson’s ratio. J Microelectromech Syst 6(2):99–106
Lim TC (2014) Semi-auxetic yarns. Phys Status Solidi B 251(2):273–280
Lim TC (2017a) Analogies across auxetic models based on deformation mechanism. Phys Status Solidi RRL 11(6):1600440
Lim TC (2017b) Auxetic and negative thermal expansion structure based on interconnected array of rings and sliding rods. Phys Status Solidi B 254(12):1600775
Lim TC (2019) Negative environmental expansion for interconnected array of rings and sliding rods. Phys Status Solidi B 256(1):1800032
Mousanezhad D, Babaee S, Ebrahimi H, Ghosh R, Hamouda AS, Bertoldi K, Vaziri A (2015) Hierarchical honeycomb auxetic metamaterials. Scient Rep 5:18306
Muto K, Bailey RW, Mitchell KJ (1963) Special requirements for the design of nuclear power stations to withstand earthquakes. Proc Inst Mech Eng 177(1):155–203
Ravirala N, Alderson A, Alderson KL (2007) Interlocking hexagon model for auxetic behavior. J Mater Sci 42(17):7433–7445
Shim J, Shan S, Kosmrlj A, Kang SH, Chen ER, Weaver JC. Bertoldi K (2013) Harnessing instabilities for design of soft reconfigurable auxetic/chiral materials. Soft Matter 9(34):8198–8202
Smith CW, Grima JN, Evans KE (2000) A novel mechanism for generating auxetic behavior in reticulated foams: missing rib foam model. Acta Mater 48(17):4349–4356
Taylor M, Francesconi L, Gerendas M, Shanian A, Carson C, Bertoldi K (2013) Low porosity metallic periodic structures with negative Poisson’s ratio. Adv Mater 26(15):2365–2370
Theocaris PS, Stavroulakis GE, Panagiotopoulos (1997) Negative Poisson’s ratios in composites with star-shaped inclusions: a numerical homogenization approach. Arch Appl Mech 67(4):274–286
Tretiakov KV, 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
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
Wojciechowski KW (1989) Two-dimensional isotropic system with a negative Poisson ratio. Phys Lett A 137(1&2):60–64
Wojciechowski KW, Branka AC (1989) Negative Poisson ratio in a two-dimensional ‘‘isotropic’’ solid. Phys Rev A 40(12):7222–7225
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Lim, TC. (2020). Analogies Across Auxetic Models. In: Mechanics of Metamaterials with Negative Parameters. Engineering Materials. Springer, Singapore. https://doi.org/10.1007/978-981-15-6446-8_3
Download citation
DOI: https://doi.org/10.1007/978-981-15-6446-8_3
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-6445-1
Online ISBN: 978-981-15-6446-8
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)