auxetics

The term auxetic derives from the Greek word {{Transliteration|el|auxetikos}} ({{lang|el|αὐξητικός}}) which means 'that which tends to increase' and has its root in the word {{Transliteration|el|auxesis}} ({{lang|el|αὔξησις}}), meaning 'increase' (noun). This terminology was coined by Professor Ken Evans of the University of Exeter.{{Citation | last = Quinion | first = Michael | title = Auxetic | date = 9 November 1996 | url = http://www.worldwidewords.org/turnsofphrase/tp-aux1.htm}}.{{Citation | last = Evans | first = Ken | title = Auxetic polymers: a new range of materials. | journal = Endeavour | date = 1991 | pages = 170–174 | doi=10.1016/0160-9327(91)90123-S | volume=15| issue = 4 }}.

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 Science in 1987, entitled "Foam structures with a Negative Poisson's Ratio"{{Citation | last = Lakes | first = R.S. | title = Foam structures with a negative Poisson's ratio | journal = Science | volume = 235 | issue = 4792 | pages = 1038–40 | date = 27 February 1987 | doi = 10.1126/science.235.4792.1038 | postscript =. | pmid = 17782252|bibcode = 1987Sci...235.1038L | s2cid = 21386778 }} by R.S. Lakes from the University of Wisconsin Madison. The use of the word auxetic to refer to this property probably began in 1991.{{Citation | last = Evans | first = Ken| title = Auxetic polymers: a new range of materials| date = 1991 | doi=10.1016/0160-9327(91)90123-S | volume=15 | issue = 4| journal=Endeavour | pages=170–174}}. Recently, cells were shown to display a biological version of auxeticity under certain conditions.{{Citation | last = Morrish | first = RB| title = Single Cell Imaging of Nuclear Architecture Changes| date = 2019 | doi=10.3389/fcell.2019.00141 | volume= 7 | journal= Front. Cell Dev. Biol. | pages= 141| pmid = 31396512| pmc = 6668442| doi-access = free}}.

Designs of composites with inverted hexagonal periodicity cell (auxetic hexagon), possessing negative Poisson ratios, were published in 1985.{{cite journal | last1 = Kolpakov | first1 = A.G. | year =1985 | title = Determination of the average characteristics of elastic frameworks | journal = Journal of Applied Mathematics and Mechanics | volume = 49 | issue = 6| pages = 739–745 | doi=10.1016/0021-8928(85)90011-5|bibcode = 1985JApMM..49..739K }}

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 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.Ren, Xin, et al. "Auxetic metamaterials and structures: a review." Smart materials and structures 27.2 (2018): 023001. 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.

Typically, auxetic materials have low density, which is what allows the hinge-like areas of the auxetic microstructures to flex.{{Cite web|url=https://www.newscientist.com/article/mg15420854-200-a-stretch-of-the-imagination/|title=A stretch of the imagination|website=New Scientist}}

At the macroscale, auxetic behaviour can be illustrated with an inelastic 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 products with enhanced characteristics such as footwear based on the auxetic rotating triangles structures developed by Grima and Evans{{Cite journal|last1=Grima|first1=JN|last2=Evans|first2=KE|year=2000|title=Auxetic behavior from rotating squares|journal=Journal of Materials Science Letters|volume=19|issue=17|pages=1563–1565|doi=10.1023/A:1006781224002|s2cid=138455050}}{{Cite journal|last1=Grima|first1=JN|last2=Evans|first2=KE|year=2006|title=Auxetic behavior from rotating triangles|journal=Journal of Materials Science|volume=41|issue=10|pages=3193–3196|doi=10.1007/s10853-006-6339-8|bibcode = 2006JMatS..41.3193G |s2cid=137547536}}{{Cite web|url=https://about.nike.com/en/newsroom|title=NIKE, Inc. Newsroom: Press Releases, Product Announcements and Media Resources —|website=about.nike.com}} and prosthetic feet with human-like toe joint properties.{{Cite journal |last1=Hong |first1=Woolim |last2=Kumar |first2=Namita Anil |last3=Patrick |first3=Shawanee |last4=Um |first4=Hui-Jin |last5=Kim |first5=Heon-Su |last6=Kim |first6=Hak-Sung |last7=Hur |first7=Pilwon |date=2022 |title=Empirical Validation of an Auxetic Structured Foot With the Powered Transfemoral Prosthesis |url=https://ieeexplore.ieee.org/document/9844236 |journal=IEEE Robotics and Automation Letters |volume=7 |issue=4 |pages=11228–11235 |doi=10.1109/LRA.2022.3194673 |s2cid=251170703 |issn=2377-3766|url-access=subscription }}

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.{{Cite journal |last1=Tripathi |first1=Kamal |last2=Menon |first2=Gautam I. |date=2019-10-28 |title=Chromatin Compaction, Auxeticity, and the Epigenetic Landscape of Stem Cells |journal=Physical Review X |volume=9 |issue=4 |pages=041020 |doi=10.1103/PhysRevX.9.041020|s2cid=209958957 |doi-access=free }}

File:Athletic Footwear with Auxetic Sole.jpg

Examples of auxetic materials include:

• Auxetic polyurethane foam{{cite journal | last1=Li | first1=Yan | last2=Zeng | first2=Changchun |title = On the successful fabrication of auxetic polyurethane foams: Materials requirement, processing strategy and conversion mechanism | journal = Polymer | year = 2016 |doi=10.1016/j.polymer.2016.01.076| volume=87 |pages=98–107}}{{cite journal | last1=Li | first1=Yan | last2=Zeng | first2=Changchun | title = Room-Temperature, Near-Instantaneous Fabrication of Auxetic Materials with Constant Poisson's Ratio over Large Deformation | journal = Advanced Materials | year = 2016 |doi=10.1002/adma.201505650| pmid=26861805 | volume=28 | issue=14 | pages=2822–2826 | s2cid=5260896 }}
• Nuclei of mouse embryonic stem cells in exiting pluripotent state
• α-Cristobalite.{{Cite journal|last1=Yeganeh-Haeri|first1=Amir|last2=Weidner|first2=Donald J.|last3=Parise|first3=John B.|date=31 July 1992|title=Elasticity of α-Cristobalite: A Silicon Dioxide with a Negative Poisson's Ratio|journal=Science|language=en|volume=257|issue=5070|pages=650–652|doi=10.1126/science.257.5070.650|issn=0036-8075|pmid=17740733|bibcode = 1992Sci...257..650Y |s2cid=137416819}}
• Certain states of crystalline materials: Li, Na, K, Cu, Rb, Ag, Fe, Ni, Co, Cs, Au, Be, Ca, Zn, Sr, Sb, MoS₂, BAsO₄, and others.{{Cite journal|last1=Goldstein|first1=R.V.|last2=Gorodtsov|first2=V.A.|last3=Lisovenko|first3=D.S.|date=2013|title=Classification of cubic auxetics|journal=Physica Status Solidi B|language=en|volume=250|issue=10|pages=2038–2043|doi=10.1002/pssb.201384233 |s2cid=117802510 }}{{Cite journal|last1=Gorodtsov|first1=V.A.|last2=Lisovenko|first2=D.S.|date=2019|title=Extreme values of Young's modulus and Poisson's ratio of hexagonal crystals|journal=Mechanics of Materials|language=en|volume=134|pages=1–8|doi=10.1016/j.mechmat.2019.03.017 |s2cid=140493258 }}{{cite journal |last1=Grima-Cornish |first1=JN |last2=Vella-Zarb |first2=L |last3=Grima |first3=JN |title=Negative Linear Compressibility and Auxeticity in Boron Arsenate |journal= Annalen der Physik|date=2020 |volume=532 |issue=5 |pages=1900550 |doi=10.1002/andp.201900550 |bibcode=2020AnP...53200550G |s2cid=216414513 }}
• Certain rocks and minerals{{Citation | last = Burke | first = Maria | title = A stretch of the imagination | journal = New Scientist | volume = 154 | issue = 2085 | page = 36 | date = 7 June 1997 | url = https://www.newscientist.com/article/mg15420854.200-a-stretch-of-the-imagination.html}}
• Graphene, which can be made auxetic through the introduction of vacancy defects{{cite journal |last1=Grima |first1=J. N. |last2=Winczewski |first2=S. |last3=Mizzi |first3=L. |last4=Grech |first4=M. C. |last5=Cauchi |first5=R. |last6=Gatt |first6=R. |last7=Attard |first7=D. |last8=Wojciechowski |first8=K.W. |last9=Rybicki |first9=J. |title=Tailoring Graphene to Achieve Negative Poisson's Ratio Properties |doi=10.1002/adma.201404106 |pmid=25504060 |journal=Advanced Materials |year=2014 |volume=27 |issue=8 |pages=1455–1459|s2cid=19738771 |hdl=11380/1239858 |hdl-access=free }}{{Cite journal|last1=Grima|first1=Joseph N.|last2=Grech|first2=Michael C.|last3=Grima-Cornish|first3=James N.|last4=Gatt|first4=Ruben|last5=Attard|first5=Daphne|date=2018|title=Giant Auxetic Behaviour in Engineered Graphene|journal=Annalen der Physik|language=en|volume=530|issue=6|pages=1700330|doi=10.1002/andp.201700330|issn=1521-3889|bibcode=2018AnP...53000330G|s2cid=125889091 }}
• Carbon diamond-like phases{{Cite journal|last1=Rysaeva|first1=L.Kh.|last2=Baimova|first2=J.A.|last3=Lisovenko|first3=D.S.|last4=Gorodtsov|first4=V.A.|last5=Dmitriev|first5=S.V.|date=2019|title=Elastic properties of fullerites and diamond-like phases|journal=Physica Status Solidi B|language=en|volume=256|issue=1|pages=1800049|doi=10.1002/pssb.201800049 |bibcode=2019PSSBR.25600049R|doi-access=}}
• Two-dimensional tungsten semicarbide{{Cite journal|last1=Stocek|first1=N.B.|last2=Ullah|first2=F.|last3=Fanchini|first3=G.|date=2024|title=Giant auxetic behavior in remote-plasma synthesized few-layer tungsten semicarbide|journal=Materials Horizons|language=en|volume=11|issue=13 |pages=3066–3075|doi=10.1039/D3MH02193A|pmid=38639038 }}
• Noncarbon nanotubes{{Cite journal|last1=Goldstein|first1=R.V.|last2=Gorodtsov|first2=V.A.|last3=Lisovenko|first3=D.S.|last4=Volkov|first4=M.A.|date=2014|title=Negative Poisson's ratio for cubic crystals and nano/microtubes|journal=Physical Mesomechanics|language=en|volume=17|issue=2|pages=97–115|doi=10.1134/S1029959914020027 |s2cid=137267947}}{{Cite journal|last1=Bryukhanov|first1=I.A.|last2=Gorodtsov|first2=V.A.|last3=Lisovenko|first3=D.S.|date=2019|title=Chiral Fe nanotubes with both negative Poisson's ratio and Poynting's effect. Atomistic simulation|journal=Journal of Physics: Condensed Matter|language=en|volume=31|issue=47|pages=475304|doi=10.1088/1361-648X/ab3a04 |pmid=31398716|bibcode=2019JPCM...31U5304B|s2cid=199519252 }}
• Living bone tissue (although this is only suspected)
• Tendons within their normal range of motion.{{cite journal | vauthors = 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 | title = Negative Poisson's ratios in tendons: An unexpected mechanical response | journal = Acta Biomater. | year = 2015 | doi = 10.1016/j.actbio.2015.06.018 | pmid = 26102335 | volume=24 | pages=201–208| url = http://eprints.staffs.ac.uk/3517/1/AA_Negative_Possionsratio_Paper_M.pdf }}
• Specific variants of polytetrafluorethylene polymers such as Gore-Tex{{Citation | title = Auxetic materials | url = http://www.azom.com/details.asp?ArticleID=168| date = 9 March 2001 }}.
• Several types of origami folds like the Diamond-Folding-Structure (RFS), the herringbone-fold-structure (FFS) or the miura fold,{{Cite book|url=http://www.markschenk.com/research/files/PhD%20thesis%20-%20Mark%20Schenk.pdf|title=Folded Shell Structures, PhD Thesis|last=Mark|first=Schenk|publisher=University of Cambridge, Clare College|year=2011}}{{Cite journal | doi=10.1038/srep05979| pmid=25099402| pmc=4124469| title=Origami based Mechanical Metamaterials| journal=Scientific Reports| volume=4| pages=5979| year=2015| last1=Lv| first1=Cheng| last2=Krishnaraju| first2=Deepakshyam| last3=Konjevod| first3=Goran| last4=Yu| first4=Hongyu| last5=Jiang| first5=Hanqing}} and other periodic patterns derived from it.{{Cite journal|title = Unraveling metamaterial properties in zigzag-base folded sheets|journal = Science Advances|date = 2015|issn = 2375-2548|pages = e1500224|volume = 1|issue = 8|doi = 10.1126/sciadv.1500224|first1 = Maryam|last1 = Eidini|first2 = Glaucio H.|last2 = Paulino|arxiv = 1502.05977 |bibcode = 2015SciA....1E0224E|pmid=26601253|pmc=4643767}}{{Cite journal|last=Eidini|first=Maryam|title=Zigzag-base folded sheet cellular mechanical metamaterials|journal=Extreme Mechanics Letters|volume=6|pages=96–102|doi=10.1016/j.eml.2015.12.006|year=2016|arxiv=1509.08104|s2cid=118424595}}

File:Meta-aux-orange.jpg. The thin rubber surface with perforated architecture covers a spherical surface (orange){{cite journal|last1=Mizzi|first1=Luke|last2=Salvati|first2=Enrico|last3=Spaggiari|first3=Andrea|last4=Tan|first4=Jin-Chong|last5=Korsunsky|first5=Alexander M.|title=Highly stretchable two-dimensional auxetic metamaterial sheets fabricated via direct-laser cutting|journal=International Journal of Mechanical Sciences|volume=167|year=2020|pages=105242|issn=0020-7403|doi=10.1016/j.ijmecsci.2019.105242|hdl=11380/1185053 |s2cid=210231091 |url=https://ora.ox.ac.uk/objects/uuid:61962177-e5f8-48c6-8eef-a3c125ec804d/download_file?safe_filename=%28aam%29Mizzi%2520-%25202D%2520auxetic%2520sheet_.pdf&file_format=application%2Fpdf&type_of_work=Journal+article|hdl-access=free}}]]

• Tailored structures designed to exhibit special designed Poisson's ratios.{{cite journal|title=Tailored 3D Mechanical Metamaterials Made by Dip-in Direct-Laser-Writing Optical Lithography|author=Tiemo Bückmann|display-authors=etal|doi=10.1002/adma.201200584|volume=24|issue=20|journal=Advanced Materials|pages=2710–2714|pmid=22495906|date=May 2012|s2cid=205244958 }}{{Cite journal|last1=Grima-Cornish|first1=James N.|last2=Grima|first2=Joseph N.|last3=Evans|first3=Kenneth E.|date=2017|title=On the Structural and Mechanical Properties of Poly(Phenylacetylene) Truss-Like Hexagonal Hierarchical Nanonetworks|journal=Physica Status Solidi B|language=en|volume=254|issue=12|pages=1700190|doi=10.1002/pssb.201700190|issn=1521-3951|bibcode=2017PSSBR.25400190G|hdl=10871/31485|s2cid=126184802 |hdl-access=free}}{{Cite journal|last1=Cabras|first1=Luigi|last2=Brun|first2=Michele|date=2014|title=Auxetic two-dimensional lattices with Poisson's ratio arbitrarily close to −1|journal=Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences|language=en|volume=470|issue=2172|pages=20140538|doi=10.1098/rspa.2014.0538|arxiv=1407.5679|bibcode=2014RSPSA.47040538C|issn=1364-5021|doi-access=free}}{{Cite journal|last1=Carta|first1=Giorgio|last2=Brun|first2=Michele|last3=Baldi|first3=Antonio|date=2016|title=Design of a porous material with isotropic negative Poisson's ratio|journal=Mechanics of Materials|language=en|volume=97|pages=67–75|doi=10.1016/j.mechmat.2016.02.012}}{{Cite journal|last1=Cabras|first1=Luigi|last2=Brun|first2=Michele|date=2016|title=A class of auxetic three-dimensional lattices|journal=Journal of the Mechanics and Physics of Solids|language=en|volume=91|pages=56–72|doi=10.1016/j.jmps.2016.02.010|arxiv=1506.04919|bibcode=2016JMPSo..91...56C|s2cid=85547530}}{{Cite journal|last1=Kaminakis|first1=N|last2=Stavroulakis|first2=G|date=2012|title=Topology optimization for compliant mechanisms, using evolutionary-hybrid algorithms and application to the design of auxetic materials|journal=Composites Part B Engineering|volume=43|issue=6|pages=2655–2668|doi=10.1016/j.compositesb.2012.03.018}}
• Chain organic molecules. Recent researches revealed that organic crystals like n-paraffins and similar to them may demonstrate an auxetic behavior.{{cite journal | last1 = Stetsenko | first1 = M | year = 2015 | title = Determining the elastic constants of hydrocarbons of heavy oil products using molecular dynamics simulation approach | journal = Journal of Petroleum Science and Engineering | volume = 126 | pages = 124–130 | doi = 10.1016/j.petrol.2014.12.021 | url = https://zenodo.org/record/889919 | doi-access = free }}

Auxetics are used in garments, origami, and chemicals.

Synthetic auxetics using a bio-inspired lattice structure (BLS) are reported to supply 13 times more stiffness, absorb 10% more energy, and exhibit a 60% greater strain range than existing auxetic materials. Potential applications include construction material, protective sports gear, and medical products.{{Cite web |last=Ghoshal |first=Abhimanyu |date=2025-03-08 |title=Sea sponges inspire super strong material for more durable buildings |url=https://newatlas.com/materials/sea-sponges-inspire-strong-material-rmit/?utm_source=New+Atlas+Subscribers&utm_campaign=9f71e55ea4-EMAIL_CAMPAIGN_2025_03_10_01_37&utm_medium=email&utm_term=0_65b67362bd-9f71e55ea4-90065621 |access-date=2025-03-13 |website=New Atlas |language=en-US}}

• Acoustic metamaterial
• Mechanical metamaterial
• Metamaterial
• Parallelogon
• Zetix, a type of commercially manufactured auxetic material

{{reflist}}

• [http://silver.neep.wisc.edu/~lakes/Poisson.html Materials with negative Poisson's ratio]
• [https://www.youtube.com/watch?v=HJ1Ck6FIqwU Auxetic foam in youtube]
• [https://web.archive.org/web/20180403214416/http://www.auxetic.info/ General Information about Auxetic Materials]

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