98:. One of the first artificially produced auxetic materials, the RFS structure (diamond-fold structure), was invented in 1978 by the Berlin researcher K. Pietsch. Although he did not use the term auxetics, he describes for the first time the underlying lever mechanism and its non-linear mechanical reaction so he is therefore considered the inventor of the auxetic net. The earliest published example of a material with negative Poisson's constant is due to A. G. Kolpakov in 1985, "Determination of the average characteristics of elastic frameworks"; the next synthetic auxetic material was described in
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121:
publications were released, so the number of publications has exploded - a 165-fold increase in just 25 years - clearly showing that the topic of
Auxetics is drawing considerable attention. However, although Auxetics are promising structures and have a lot of potential in science and engineering, their widespread application in multiple fields is still a challenge. Therefore, additional research related to Auxetics is required for widespread applications.
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Auxetic materials are used in protective equipment such as body armor, helmets, and knee pads, as they absorb energy more effectively than traditional materials. They are also used in devices such as medical stents or implants. Auxetic fabrics can be used to create comfortable and flexible clothing,
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string wound around an elastic cord. When the ends of the structure are pulled apart, the inelastic string straightens while the elastic cord stretches and winds around it, increasing the structure's effective volume. Auxetic behaviour at the macroscale can also be employed for the development of
120:
For these reasons, gradually, many researchers have become interested in the unique properties of
Auxetics. This phenomenon is visible in the number of publications (Scopus search engine), as shown in the following figure. In 1991, there was only one publication. However, in 2016, around 165
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Auxetic materials also occur organically, although they are structurally different from man-made metamaterials. For example, the nuclei of mouse embryonic stem cells in a transition state display auxetic behavior.
1028:
Grima, J. N.; Winczewski, S.; Mizzi, L.; Grech, M. C.; Cauchi, R.; Gatt, R.; Attard, D.; Wojciechowski, K.W.; Rybicki, J. (2014). "Tailoring
Graphene to Achieve Negative Poisson's Ratio Properties".
141:
products with enhanced characteristics such as footwear based on the auxetic rotating triangles structures developed by Grima and Evans and prosthetic feet with human-like toe joint properties.
1591:
Grima‐Cornish, James N.; Grima, Joseph N.; Evans, Kenneth E. (2017). "On the
Structural and Mechanical Properties of Poly(Phenylacetylene) Truss-Like Hexagonal Hierarchical Nanonetworks".
1791:
Kaminakis, N; Stavroulakis, G (2012). "Topology optimization for compliant mechanisms, using evolutionary-hybrid algorithms and application to the design of auxetic materials".
39:, so that axial elongation causes transversal elongation (in contrast to an ordinary material, where stretching in one direction causes compression in the other direction).
760:
Li, Yan; Zeng, Changchun (2016). "On the successful fabrication of auxetic polyurethane foams: Materials requirement, processing strategy and conversion mechanism".
1192:
Bryukhanov, I.A.; Gorodtsov, V.A.; Lisovenko, D.S. (2019). "Chiral Fe nanotubes with both negative
Poisson's ratio and Poynting's effect. Atomistic simulation".
787:
Li, Yan; Zeng, Changchun (2016). "Room‐Temperature, Near‐Instantaneous
Fabrication of Auxetic Materials with Constant Poisson's Ratio over Large Deformation".
830:
Yeganeh-Haeri, Amir; Weidner, Donald J.; Parise, John B. (31 July 1992). "Elasticity of α-Cristobalite: A Silicon
Dioxide with a Negative Poisson's Ratio".
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to refer to this property probably began in 1991. Recently, cells were shown to display a biological version of auxeticity under certain conditions.
1122:
Rysaeva, L.Kh.; Baimova, J.A.; Lisovenko, D.S.; Gorodtsov, V.A.; Dmitriev, S.V. (2019). "Elastic properties of fullerites and diamond-like phases".
1071:
Grima, Joseph N.; Grech, Michael C.; Grima‐Cornish, James N.; Gatt, Ruben; Attard, Daphne (2018). "Giant
Auxetic Behaviour in Engineered Graphene".
1243:
Gatt R, Vella Wood M, Gatt A, Zarb F, Formosa C, Azzopardi KM, Casha A, Agius TP, Schembri-Wismayer P, Attard L, Chockalingam N, Grima JN (2015).
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Designs of composites with inverted hexagonal periodicity cell (auxetic hexagon), possessing negative
Poisson ratios, were published in 1985.
1157:
Goldstein, R.V.; Gorodtsov, V.A.; Lisovenko, D.S.; Volkov, M.A. (2014). "Negative
Poisson's ratio for cubic crystals and nano/microtubes".
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Tiemo Bückmann; et al. (May 2012). "Tailored 3D Mechanical Metamaterials Made by Dip-in Direct-Laser-Writing Optical Lithography".
50:
as well as technical fabrics for applications such as aerospace and sports equipment. Auxetic materials can also be used to create
107:
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Carta, Giorgio; Brun, Michele; Baldi, Antonio (2016). "Design of a porous material with isotropic negative Poisson's ratio".
1006:
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Grima-Cornish, JN; Vella-Zarb, L; Grima, JN (2020). "Negative Linear Compressibility and Auxeticity in Boron Arsenate".
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Gorodtsov, V.A.; Lisovenko, D.S. (2019). "Extreme values of Young's modulus and Poisson's ratio of hexagonal crystals".
565:
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In footwear, auxetic design allows the sole to expand in size while walking or running, thereby increasing flexibility.
1820:"Determining the elastic constants of hydrocarbons of heavy oil products using molecular dynamics simulation approach"
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Ren, Xin, et al. "Auxetic metamaterials and structures: a review." Smart materials and structures 27.2 (2018): 023001.
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Hong, Woolim; Kumar, Namita Anil; Patrick, Shawanee; Um, Hui-Jin; Kim, Heon-Su; Kim, Hak-Sung; Hur, Pilwon (2022).
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Production of auxetic metamaterials through the introduction of patterned microstructural cuts using direct
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Certain states of crystalline materials: Li, Na, K, Cu, Rb, Ag, Fe, Ni, Co, Cs, Au, Be, Ca, Zn, Sr, Sb, MoS
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1493:"Highly stretchable two-dimensional auxetic metamaterial sheets fabricated via direct-laser cutting"
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Mizzi, Luke; Salvati, Enrico; Spaggiari, Andrea; Tan, Jin-Chong; Korsunsky, Alexander M. (2020).
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Goldstein, R.V.; Gorodtsov, V.A.; Lisovenko, D.S. (2013). "Classification of cubic auxetics".
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671:"Empirical Validation of an Auxetic Structured Foot With the Powered Transfemoral Prosthesis"
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Kolpakov, A.G. (1985). "Determination of the average characteristics of elastic frameworks".
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243:. The thin rubber surface with perforated architecture covers a spherical surface (orange)
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Lv, Cheng; Krishnaraju, Deepakshyam; Konjevod, Goran; Yu, Hongyu; Jiang, Hanqing (2015).
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94:), meaning 'increase' (noun). This terminology was coined by Professor Ken Evans of the
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67:
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Cabras, Luigi; Brun, Michele (2016). "A class of auxetic three-dimensional lattices".
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Liu, Yangzuo; Zhao, Changfang; Xu, Cheng; Ren, Jie; Zhong, Jianlin (1 December 2023).
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Eidini, Maryam (2016). "Zigzag-base folded sheet cellular mechanical metamaterials".
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Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
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Lakes, R.S. (27 February 1987), "Foam structures with a negative Poisson's ratio",
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Chain organic molecules. Recent researches revealed that organic crystals like n-
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1654:"Auxetic two-dimensional lattices with Poisson's ratio arbitrarily close to −1"
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721:"Chromatin Compaction, Auxeticity, and the Epigenetic Landscape of Stem Cells"
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Several types of origami folds like the Diamond-Folding-Structure (RFS), the
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Morrish, RB (2019), "Single Cell Imaging of Nuclear Architecture Changes",
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Tailored structures designed to exhibit special designed Poisson's ratios.
82:) which means 'that which tends to increase' and has its root in the word
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1245:"Negative Poisson's ratios in tendons: An unexpected mechanical response"
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Grima, JN; Evans, KE (2006). "Auxetic behavior from rotating triangles".
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Grima, JN; Evans, KE (2000). "Auxetic behavior from rotating squares".
198:, which can be made auxetic through the introduction of vacancy defects
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392:"Auxetic meta-materials and their engineering applications: a review"
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structures with a Negative Poisson's Ratio" by R.S. Lakes from the
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Evans, Ken (1991), "Auxetic polymers: a new range of materials.",
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Nuclei of mouse embryonic stem cells in exiting pluripotent state
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1373:"Unraveling metamaterial properties in zigzag-base folded sheets"
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Evans, Ken (1991), "Auxetic polymers: a new range of materials",
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A stretch of the imagination – 7 June 1997 – New Scientist Space
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At the macroscale, auxetic behaviour can be illustrated with an
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46:, crystals, or a particular structure of macroscopic matter.
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and similar to them may demonstrate an auxetic behavior.
288:, a type of commercially manufactured auxetic material
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Tripathi, Kamal; Menon, Gautam I. (28 October 2019).
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Living bone tissue (although this is only suspected)
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1740:Journal of the Mechanics and Physics of Solids
231:, and other periodic patterns derived from it.
16:Materials that have a negative Poisson's ratio
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1824:Journal of Petroleum Science and Engineering
1497:International Journal of Mechanical Sciences
1371:Eidini, Maryam; Paulino, Glaucio H. (2015).
524:Journal of Applied Mathematics and Mechanics
210:Tendons within their normal range of motion.
1865:General Information about Auxetic Materials
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1311:. University of Cambridge, Clare College.
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1324:"Origami based Mechanical Metamaterials"
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1855:Materials with negative Poisson's ratio
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161:Examples of auxetic materials include:
656:"Nike Free 2016 product press release"
129:Typically, auxetic materials have low
1652:Cabras, Luigi; Brun, Michele (2014).
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54:for controlling sound and vibration.
7:
1194:Journal of Physics: Condensed Matter
675:IEEE Robotics and Automation Letters
579:Journal of Materials Science Letters
431:Quinion, Michael (9 November 1996),
1305:Folded Shell Structures, PhD Thesis
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1805:10.1016/j.compositesb.2012.03.018
108:University of Wisconsin Madison
1509:10.1016/j.ijmecsci.2019.105242
1007:"A stretch of the imagination"
1:
1793:Composites Part B Engineering
1725:10.1016/j.mechmat.2016.02.012
938:10.1016/j.mechmat.2019.03.017
774:10.1016/j.polymer.2016.01.076
331:10.1126/science.235.4792.1038
227:-fold-structure (FFS) or the
1837:10.1016/j.petrol.2014.12.021
1264:10.1016/j.actbio.2015.06.018
1005:Burke, Maria (7 June 1997),
852:10.1126/science.257.5070.650
614:Journal of Materials Science
544:10.1016/0021-8928(85)90011-5
462:10.1016/0160-9327(91)90123-S
396:Engineering Research Express
377:10.1016/0160-9327(91)90123-S
84:
72:
1901:
1770:10.1016/j.jmps.2016.02.010
201:Carbon diamond-like phases
192:Certain rocks and minerals
1470:10.1016/j.eml.2015.12.006
1448:Extreme Mechanics Letters
1171:10.1134/S1029959914020027
738:10.1103/PhysRevX.9.041020
634:10.1007/s10853-006-6339-8
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1214:10.1088/1361-648X/ab3a04
687:10.1109/LRA.2022.3194673
490:10.3389/fcell.2019.00141
409:10.1088/2631-8695/ad0eb1
1860:Auxetic foam in youtube
1593:Physica Status Solidi B
1124:Physica Status Solidi B
891:Physica Status Solidi B
591:10.1023/A:1006781224002
271:Mechanical metamaterial
42:Auxetics can be single
1713:Mechanics of Materials
1689:10.1098/rspa.2014.0538
1613:10.1002/pssb.201700190
1562:10.1002/adma.201200584
1407:10.1126/sciadv.1500224
1159:Physical Mesomechanics
1144:10.1002/pssb.201800049
1093:10.1002/andp.201700330
1042:10.1002/adma.201404106
981:10.1002/andp.201900550
926:Mechanics of Materials
903:10.1002/pssb.201384233
801:10.1002/adma.201505650
477:Front. Cell Dev. Biol.
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215:polytetrafluorethylene
158:
110:. The use of the word
52:acoustic metamaterials
25:
1818:Stetsenko, M (2015).
1302:Mark, Schenk (2011).
266:Acoustic metamaterial
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213:Specific variants of
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29:Auxetic metamaterials
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96:University of Exeter
1762:2016JMPSo..91...56C
1680:2014RSPSA.47040538C
1605:2017PSSBR.25400190G
1399:2015SciA....1E0224E
1206:2019JPCM...31U5304B
1136:2019PSSBR.25600049R
1085:2018AnP...53000330G
973:2020AnP...53200550G
844:1992Sci...257..650Y
626:2006JMatS..41.3193G
536:1985JApMM..49..739K
323:1987Sci...235.1038L
204:Noncarbon nanotubes
102:in 1987, entitled "
1664:(2172): 20140538.
1550:Advanced Materials
1328:Scientific Reports
1073:Annalen der Physik
1030:Advanced Materials
961:Annalen der Physik
789:Advanced Materials
681:(4): 11228–11235.
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1556:(20): 2710–2714.
1340:10.1038/srep05979
1287:Auxetic materials
897:(10): 2038–2043.
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795:(14): 2822–2826.
725:Physical Review X
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217:polymers such as
66:derives from the
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281:Parallelogon
276:Metamaterial
167:polyurethane
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41:
33:metamaterial
28:
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18:
1830:: 124–130.
1622:10871/31485
1258:: 201–208.
225:herringbone
1874:Categories
1753:1506.04919
1503:: 105242.
1461:1509.08104
1454:: 96–102.
1390:1502.05977
1017:(2085): 36
768:: 98–107.
293:References
229:miura fold
125:Properties
1880:Materials
1746:: 56–72.
1719:: 67–75.
1698:1364-5021
1671:1407.5679
1639:126184802
1631:1521-3951
1578:205244958
1535:210231091
1527:0020-7403
1478:118424595
1415:2375-2548
1230:199519252
1179:137267947
1109:125889091
1101:1521-3889
989:216414513
946:140493258
911:117802510
876:137416819
860:0036-8075
747:209958957
703:251170703
695:2377-3766
642:137547536
599:138455050
450:Endeavour
418:2631-8695
365:Endeavour
253:paraffins
138:inelastic
79:αὐξητικός
73:auxetikos
62:The term
44:molecules
1778:85547530
1570:22495906
1433:26601253
1358:25099402
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1272:26102335
1222:31398716
1058:19738771
1050:25504060
868:17740733
809:26861805
509:31396512
347:21386778
339:17782252
260:See also
219:Gore-Tex
196:Graphene
165:Auxetic
149:Examples
1758:Bibcode
1676:Bibcode
1601:Bibcode
1424:4643767
1395:Bibcode
1349:4124469
1202:Bibcode
1132:Bibcode
1081:Bibcode
969:Bibcode
932:: 1–8.
840:Bibcode
832:Science
817:5260896
762:Polymer
622:Bibcode
532:Bibcode
500:6668442
483:: 141,
434:Auxetic
319:Bibcode
311:Science
131:density
112:auxetic
100:Science
91:αὔξησις
85:auxesis
64:auxetic
58:History
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1696:
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185:, BAsO
1774:S2CID
1748:arXiv
1666:arXiv
1635:S2CID
1574:S2CID
1531:S2CID
1474:S2CID
1456:arXiv
1385:arXiv
1309:(PDF)
1248:(PDF)
1226:S2CID
1175:S2CID
1105:S2CID
1054:S2CID
985:S2CID
942:S2CID
907:S2CID
872:S2CID
813:S2CID
743:S2CID
699:S2CID
638:S2CID
595:S2CID
343:S2CID
286:Zetix
70:word
68:Greek
1694:ISSN
1627:ISSN
1566:PMID
1523:ISSN
1429:PMID
1411:ISSN
1354:PMID
1268:PMID
1218:PMID
1097:ISSN
1046:PMID
864:PMID
856:ISSN
805:PMID
691:ISSN
505:PMID
414:ISSN
335:PMID
169:foam
104:Foam
1832:doi
1828:126
1801:doi
1766:doi
1721:doi
1684:doi
1662:470
1617:hdl
1609:doi
1597:254
1558:doi
1513:hdl
1505:doi
1501:167
1466:doi
1419:PMC
1403:doi
1344:PMC
1336:doi
1260:doi
1210:doi
1167:doi
1140:doi
1128:256
1089:doi
1077:530
1038:doi
1015:154
977:doi
965:532
934:doi
930:134
899:doi
895:250
848:doi
836:257
797:doi
770:doi
733:doi
683:doi
630:doi
587:doi
540:doi
495:PMC
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