Auxetic materials — A review

V. Carneiro 1 , J. Meireles 1 ,  and H. Puga 1
  • 1 Department of Mechanics Engineering, University of Minho, Campus de Azurém, Guimarăes, Portugal

Abstract

Auxetic materials are endowed with a behavior that contradicts common sense, when subjected to an axial tensile load they increase their transverse dimension. In case of a compression load, they reduce their transverse dimension. Consequently, these materials have a negative Poisson’s ratio in such direction. This paper reviews research related to these materials. It presents the theories that explain their deformation behavior and reveals the important role represented by the internal structure. Their mechanical properties are explored and some potential applications for these materials are shown.

If the inline PDF is not rendering correctly, you can download the PDF file here.

  • [1] Roh J.H., Giller C.B., Mott P.H., Roland C.M., AIP Advances, 3 (2013), 042126. http://dx.doi.org/10.1063/1.4802925

  • [2] Greaves G.N., Greer A.L., Lakes R.S., Rouxel T., Nat. Mater., 10 (2011), 823. http://dx.doi.org/10.1038/nmat3134

  • [3] Strek T., Maruszewski B., Narojczyk J.W., Wojciechowski K.W., J. Non-Cryst. Solids, 354 (2008), 4475. http://dx.doi.org/10.1016/j.jnoncrysol.2008.06.087

  • [4] Wojciechowski K.W., Novikov V.V., Task Quarterly, 5 (2001), 5.

  • [5] Gercek H., Int. J. Rock Mech. Min., 44 (2007), 1. http://dx.doi.org/10.1016/j.ijrmms.2006.04.011

  • [6] Glieck J., The New York Times, 14th April 1987.

  • [7] Milton G.W., J. Mech. Phys. Solids, 40 (1992), 1105. http://dx.doi.org/10.1016/0022-5096(92)90063-8

  • [8] Evans K.E., Nkansah M.A., Hutchinson I.J., Rogers S.C., Nature, 353 (1991), 124. http://dx.doi.org/10.1038/353124a0

  • [9] Prawoto Y., Comp. Mater. Sci., 58 (2012), 140. http://dx.doi.org/10.1016/j.commatsci.2012.02.012

  • [10] Wojciechowski, K.W., J. Phys. Soc. Jpn., 72 (2003), 1819. http://dx.doi.org/10.1143/JPSJ.72.1819

  • [11] Kocer C., Mckenzie D.R., Bilek M.M., Mater. Sci. Eng. A — Struct., 505 (2009), 111. http://dx.doi.org/10.1016/j.msea.2008.11.002

  • [12] Mott P.H., Roland C.M., Phys. Scripta, 87 (2013), 055404. http://dx.doi.org/10.1088/0031-8949/87/05/055404

  • [13] Lakes R.S., Lee T., Bersie A., Wang Y.C., Nature, 410 (2001), 565. http://dx.doi.org/10.1038/35069035

  • [14] Tokmakova S.P., Phys. Stat. Sol. B, 242 (2005), 721. http://dx.doi.org/10.1002/pssb.200460389

  • [15] Narojczyk J.W., Wojciechowski K.W., Phys. Stat. Sol. B, 245 (2008), 606. http://dx.doi.org/10.1002/pssb.200777711

  • [16] Branka A.C., Heyes D.M., Mackowiak Sz., Pieprzyk S., Wojciechowski K.W., Phys. Stat. Sol. B, 249 (2012), 1373. http://dx.doi.org/10.1002/pssb.201084222

  • [17] Kimikuza H., Ogata S., Shibutani Y., Mat. T. JIM, 46 (2005), 1161. http://dx.doi.org/10.2320/matertrans.46.1161

  • [18] Narojczyk J.W., Wojciechowski K.W., J. Non-Cryst. Solids, 356 (2010), 2026. http://dx.doi.org/10.1016/j.jnoncrysol.2010.05.080

  • [19] Branka A.C., Heyes D.M., Mackowiak Sz., Pieprzyk S., Wojciechowski K.W., Phys. Stat. Sol. B, 248 (2011), 96. http://dx.doi.org/10.1002/pssb.201083981

  • [20] Baughman R.H., Shacklette J.M., Zakhidov A.A., Stafström S., Nature, 392 (1998), 362. http://dx.doi.org/10.1038/32842

  • [21] Ting T.C.T., Chen T.Y., Q. J. Mech. Appl. Math., 58 (2005), 73. http://dx.doi.org/10.1093/qjmamj/hbh021

  • [22] Norris A.N., J. Mech. Mater. Struct., 1 (2006), 793. http://dx.doi.org/10.2140/jomms.2006.1.793

  • [23] Attard D., Grima J.N., Phys. Stat. Sol. B, 245 (2008), 2395. http://dx.doi.org/10.1002/pssb.200880269

  • [24] Evans K.E., Membr Tech., 137 (2001), 9. http://dx.doi.org/10.1016/S0958-2118(01)80300-1

  • [25] Voigt W., Annalen der Physik, 16 (1882), 273. http://dx.doi.org/10.1002/andp.18822520607

  • [26] Love A.E.H., A Treatise on the Mathematical Theory of Elasticity, Dover Publications, United States of America, 1944

  • [27] Kimizuka H., Kaburaki H., Kogure Y., Phys. Rev. Lett., 84 (2000), 5548. http://dx.doi.org/10.1103/PhysRevLett.84.5548

  • [28] Grima J.N., Evans K.E., J. Mater. Sci., 41 (2006), 3193. http://dx.doi.org/10.1007/s10853-006-6339-8

  • [29] Grima J.N., Gatt R., Alderson A., Evans K.E., J. Mater. Chem., 15 (2005), 4003. http://dx.doi.org/10.1039/b508098c

  • [30] Veronda D.R., Westmann R.A., J. Biomech., 3 (1970), 111. http://dx.doi.org/10.1016/0021-9290(70)90055-2

  • [31] Lees C., Vincent J.F.V., Hillerton J.E., Bio-Med. Mater. Eng., 1 (1991), 19.

  • [32] Williams J.L., Lewis J.L., J. Biomech. Eng., 104 (1982), 50. http://dx.doi.org/10.1115/1.3138303

  • [33] Pikhitsa P.V., Phys. Rev. Lett., 93 (2004), 015505. http://dx.doi.org/10.1103/PhysRevLett.93.015505

  • [34] Pasternak E., Diskin A.V., Int. J. Eng. Sci., 52 (2012), 103. http://dx.doi.org/10.1016/j.ijengsci.2011.11.006

  • [35] Lakes R.S., Science, 235 (1987), 1038. http://dx.doi.org/10.1126/science.235.4792.1038

  • [36] Grima J.N., Auxetic Metamaterials, Strasbourg, France, 2010

  • [37] Gaspar N., Smith C.W., Alderson A., Grima J.N., J. Mater. Sci., 46 (2011), 372. http://dx.doi.org/10.1007/s10853-010-4846-0

  • [38] Mishnaevski JR. L., Rev Adv Mater Sci., 30 (2012), 60.

  • [39] Coluci V.R., Hall L.J., Kozlov M.E., Zhang M., Dantas S.O., Galvă O D.S., Baughman R.H., Phys. Rev. B., 78 (2008), 115408. http://dx.doi.org/10.1103/PhysRevB.78.115408

  • [40] Almgren R.F., J. Elasticity, 15 (1985), 427. http://dx.doi.org/10.1007/BF00042531

  • [41] Gibson L.J., J. Biomech., 38 (2005), 377. http://dx.doi.org/10.1016/j.jbiomech.2004.09.027

  • [42] Grima J.N., Alderson A., Evans K.E., Comp. Meth Sci. Tech., 10 (2004), 137.

  • [43] Wojciechowski K.W., Mol. Phys., 61 (1987), 1247. http://dx.doi.org/10.1080/00268978700101761

  • [44] Wojciechowski K.W., Branka A.C., Phys. Rev. A, 40 (1989), 7222. http://dx.doi.org/10.1103/PhysRevA.40.7222

  • [45] Wojciechowski K.W., Phys. Lett. A, 137 (1989), 60. http://dx.doi.org/10.1016/0375-9601(89)90971-7

  • [46] Gaspar N., Ren X.Z., Smith C.W., Grima J.N., Evans K.E., Acta Mater., 53 (2005), 2439. http://dx.doi.org/10.1016/j.actamat.2005.02.006

  • [47] Wojciechowski K.W., J. Phys. A — Math. Gen., 36 (2003), 11765. http://dx.doi.org/10.1088/0305-4470/36/47/005

  • [48] Friis E.A., Lakes R.S., Park J.B., J. Mater. Sci., 23 (1988), 4406. http://dx.doi.org/10.1007/BF00551939

  • [49] Y. Liu, H. Hu., Sci. Res. Essays., 5 (2010), 1052.

  • [50] Attard D., Grima J.N., Phys. Stat. Sol. B., 248 (2011), 52. http://dx.doi.org/10.1002/pssb.201083980

  • [51] Grima J.N., Gatt R., Ellul B., Chetcuti E., J. Non-Cryst. Solids, 356 (2010), 1980. http://dx.doi.org/10.1016/j.jnoncrysol.2010.05.074

  • [52] Dmitriev S.V., Ferroelectrics, 349 (2007), 33. http://dx.doi.org/10.1080/00150190701260660

  • [53] Attard D., Manicaro E., Gatt R., Grima J.N., Phys. Stat. Sol. B, 246 (2009), 2045. http://dx.doi.org/10.1002/pssb.200982035

  • [54] Attard D., Grima J.N., Phys. Stat. Sol. B, 249 (2012), 1330. http://dx.doi.org/10.1002/pssb.201084223

  • [55] Abramovitch H., Burgard M., Azulay L.E., Evans K.E., Hoffmeister M., Miller W., Scarpa F., Smith C.W., Tee K.F., Schönecker A., Seffner L., Proceedings of SPIE., 6935 (2008), 693506. http://dx.doi.org/10.1117/12.775588

  • [56] Prall D., Lakes R.S., Int. J. Mech. Sci., 39 (1997), 305. http://dx.doi.org/10.1016/S0020-7403(96)00025-2

  • [57] F. Scarpa, Blain S., Lew T., Perrot D., Ruzzene M., Yates J.R., Compos Part A — Appl. S., 38 (2007), 280. http://dx.doi.org/10.1016/j.compositesa.2006.04.007

  • [58] Spadoni A., Ruzzene M., J. Mech. Phys. Solids, 60 (2012), 156. http://dx.doi.org/10.1016/j.jmps.2011.09.012

  • [59] Hall L.J., Coluci V.R., Galvăo D.S., Kozlov M.E., Zhang M., Dantas S.O., Baughman R.H., Science, 320 (2008), 504. http://dx.doi.org/10.1126/science.1149815

  • [60] Harkati E.H., Bezazi A., Scarpa F., Alderson K., Alderson A., Phys. Stat. Sol. B, 244 (2007), 883. http://dx.doi.org/10.1002/pssb.200572707

  • [61] Evans K.E., Alderson A., Adv. Mater., 12 (2000), 617. http://dx.doi.org/10.1002/(SICI)1521-4095(200005)12:9<617::AID-ADMA617>3.0.CO;2-3

  • [62] Argatov I.I., Díaz R.G., Sabina F.J., Int. J. Eng. Sci., 54 (2012), 42. http://dx.doi.org/10.1016/j.ijengsci.2012.01.010

  • [63] Coenen V.L., Alderson K.L., Phys. Stat. Sol. B, 248 (2011), 66. http://dx.doi.org/10.1002/pssb.201083977

  • [64] Alderson A., Chem Ind., 10 (1999), 384.

  • [65] Liu Q., Literature Review: Materials with Negative Poisson’s Ratios and Potential Applications to Aerospace and Defense, Defense Science and Technology Organization, Victoria, Australia, 2006

  • [66] Critchley R., Corni I., Wharton J.A., Walsh F.C., Wood R.J.K., Stokes K.R., Phys. Stat. Sol. B, (2013), 1.

  • [67] Tetriakov K.V., Wojciechowski K.W., J. Chem. Phys., 136 (2012), 204506. http://dx.doi.org/10.1063/1.4722100

  • [68] Narojczyk J.W., Alderson A., Imre A.R., Scrapa F., Wojciechowski K.W., J. Non-Cryst. Solids, 354 (2008), 4242. http://dx.doi.org/10.1016/j.jnoncrysol.2008.06.085

  • [69] Yang W., Li Z.L., Shi W., Xie B., Yang M., J. Mater. Sci., 39 (2004), 3269. http://dx.doi.org/10.1023/B:JMSC.0000026928.93231.e0

  • [70] Beer F.P., Johnston E.R., Mechanics of Materials, 3rd ed., MAKRON Books, Săo Paulo, Brazil, 1967

  • [71] Xinchun S., Lakes R.S., Phys. Stat. Sol. B, 244 (2007), 1008. http://dx.doi.org/10.1002/pssb.200572719

  • [72] Wang Y.C., Lakes R.S., J. Compos. Mater, 39 (2005), 1645. http://dx.doi.org/10.1177/0021998305051112

  • [73] Choi J.B., Lakes R.S., Int. J. Fracture, 80 (1996), 73. http://dx.doi.org/10.1007/BF00036481

  • [74] Bezazi A., Boukharouba W., Scarpa F., Phys. Stat. Sol. B, 246 (2009), 2102. http://dx.doi.org/10.1002/pssb.200982042

  • [75] Choi J.B., Lakes R.S., J. Mater. Sci., 27 (1992), 5373–5381

  • [76] Donoghue J.P., Alderson K.L., Evans K.E., Phys. Stat. Sol. B, 246 (2009), 2011. http://dx.doi.org/10.1002/pssb.200982031

  • [77] Miati S., Ashby M.F., Gibson L.J., Scripta Metall, 18 (1987), 213. http://dx.doi.org/10.1016/0036-9748(84)90510-6

  • [78] Haberman M.R., Hook D.T., Timothy D., J. Acoust. Soc. Am., 132 (2012), 1961. http://dx.doi.org/10.1121/1.4755220

  • [79] Howell B., Prendergast P., Hansen L., Acoustic Behavior of Negative Poisson’s Ratio Materials, Ship Materials Engineering Department — United States Navy, Arlington, United States of America, 1991.

  • [80] Chekkal I., Bianchi M., Remillat M., BÉCOT F., Jaouen L., Scarpa F., Acta Acust., 96 (2010), 266. http://dx.doi.org/10.3813/AAA.918276

  • [81] Alderson K.L., Webber R.S., Mohammed U.F., Murphy E., Evans K.E., Appl. Acoust., 50 (1997), 23. http://dx.doi.org/10.1016/S0003-682X(96)00023-0

  • [82] Ruzzene M., Scarpa F., Phys. Stat. Sol. B, 242 (2005), 665. http://dx.doi.org/10.1002/pssb.200460385

  • [83] Grima J.N., Modelling Auxetic Materials, Gdansk, Poland, 2009

  • [84] Chen Y.J., Scarpa F., Farrow I.R., Liu Y.J., Leng J.S., Smart Mater. Struct., 22 (2013), 045005. http://dx.doi.org/10.1088/0964-1726/22/4/045005

  • [85] Alderson A., Alderson K.L., Chirima G., Ravirala N., Zied K.M., Compos. Sci. Technol., 70 (2010), 1034. http://dx.doi.org/10.1016/j.compscitech.2009.07.010

  • [86] Lakes R.S., Witt R., Int. J. Mech. Eng. Edu., 30 (2002), 50. http://dx.doi.org/10.7227/IJMEE.30.1.5

  • [87] Lorato A., Innocenti P., Scarpa F., Alderson A., Alderson K.L., Zied K.M., Ravirala N., Miller W., Smith S.W., Evans K.E., Compos. Sci. Technol., 70 (2010), 1057. http://dx.doi.org/10.1016/j.compscitech.2009.07.008

  • [88] Hassan M.R., Scarpa F., Mohamed N.A, Ruzzene M., Phys. Stat. Sol. B, 245 (2008), 2440. http://dx.doi.org/10.1002/pssb.200880263

  • [89] Jacobs S., Coconnier C., Dimaio D., Scarpa F., Toso M., Martinez J., Smart Mater. Struct., 21 (2012), 075013. http://dx.doi.org/10.1088/0964-1726/21/7/075013

  • [90] Bianchi M., Scarpa F., Smith C.W., Acta Mater., 58 (2010), 858. http://dx.doi.org/10.1016/j.actamat.2009.09.063

  • [91] Bianchi M., Scarpa F., Smith C.W., Whittel G.R., J. Mater. Sci., 45 (2010), 341. http://dx.doi.org/10.1007/s10853-009-3940-7

  • [92] Alderson A., Alderson K.L., Mcdonald S.A., Mottershead B., Nazare S., Withers P.J., Yao Y.T., Macromol. Mater. Eng., 298 (2013), 318. http://dx.doi.org/10.1002/mame.201200028

  • [93] Bianchi M., Frontoni S., Scarpa F., Smith C.W., Phys. Stat. Sol. B, 248 (2011), 30. http://dx.doi.org/10.1002/pssb.201083966

  • [94] Uzun M., Patel I., Arch, Mater. Sci. Eng., 44 (2010), 120.

  • [95] Kopyt P., Damian R., Celuch M., Ciobanu R., Compos. Sci. Technol., 70 (2010), 1080. http://dx.doi.org/10.1016/j.compscitech.2009.08.017

  • [96] Bertoldi K., Reis P.M., Willshaw S., Mullin T., Adv. Mater., 22 (2010), 361. http://dx.doi.org/10.1002/adma.200901956

  • [97] Xu B., Arias F., Brittain S.T., Zhao X.-M., Grzybowski B., Torquato S., Whitesides M., Adv Mater., 11 (1999), 1186. http://dx.doi.org/10.1002/(SICI)1521-4095(199910)11:14<1186::AID-ADMA1186>3.0.CO;2-K

  • [98] Alderson A., Rasburn J., Evans K.E., Grima J.N., Membr. Tech., 137 (2001), 6. http://dx.doi.org/10.1016/S0958-2118(01)80299-8

  • [99] Evans K.E., Alderson A., Adv Mater., 12 (2000), 617. http://dx.doi.org/10.1002/(SICI)1521-4095(200005)12:9<617::AID-ADMA617>3.0.CO;2-3

  • [100] Choi J.B., Lakes R.S., Cell Polym., 10 (1991), 205.

  • [101] Alderson K.L., Alderson A., Anand S., Simkins V., Nazare S., Ravirala N., Phys. Stat. Sol. B, 249 (2012), 1322. http://dx.doi.org/10.1002/pssb.201084216

  • [102] Alderson A., Alderson K.L., Tech. Textiles Int., 77 (2005), 29.

  • [103] Simkins V.R., Alderson A., Davies P.J., Alderson K.L., J. Mater. Sci., 40 (2005), 4355. http://dx.doi.org/10.1007/s10853-005-2829-3

  • [104] Liu Y., Text. Res. J., (2009), 1.

  • [105] Yao Y.T., Alderson A., Alderson K.L., Phys. Stat. Sol. B, 245 (2008), 2373. http://dx.doi.org/10.1002/pssb.200880266

  • [106] Scarpa F., Narojczyk J.W., Wojciechowski K.W., Phys. Stat. Sol. B, 248 (2011), 82. http://dx.doi.org/10.1002/pssb.201083984

OPEN ACCESS

Journal + Issues

Search