{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,23]],"date-time":"2026-09-23T19:17:43Z","timestamp":1790191063615,"version":"4.1.0"},"reference-count":34,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2017,12,11]],"date-time":"2017-12-11T00:00:00Z","timestamp":1512950400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/academic.oup.com\/journals\/pages\/about_us\/legal\/notices"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1319389"],"award-info":[{"award-number":["1319389"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1704285"],"award-info":[{"award-number":["1704285"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1319366"],"award-info":[{"award-number":["1319366"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1703765 to I.S"],"award-info":[{"award-number":["1703765 to I.S"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000002","name":"National Institutes of Health","doi-asserted-by":"publisher","award":["1R01GM109456 to C.S.B."],"award-info":[{"award-number":["1R01GM109456 to C.S.B."]}],"id":[{"id":"10.13039\/100000002","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,5,1]]},"DOI":"10.1093\/qjmam\/hbx028","type":"journal-article","created":{"date-parts":[[2017,11,17]],"date-time":"2017-11-17T07:10:05Z","timestamp":1510902605000},"page":"125-138","source":"Crossref","is-referenced-by-count":15,"title":["Periodic Auxetics: Structure and Design"],"prefix":"10.1093","volume":"71","author":[{"given":"Ciprian S","family":"Borcea","sequence":"first","affiliation":[{"name":"Department of Mathematics, Rider University, 2083 Lawrenceville Road, Lawrenceville, NJ 08648, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ileana","family":"Streinu","sequence":"additional","affiliation":[{"name":"Computer Science Department, Smith College, 10 Elm Street, Northampton, MA 01063, USA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2017,12,11]]},"reference":[{"key":"key\n\t\t\t\t20180507100047_B1","doi-asserted-by":"crossref","first-page":"1038","DOI":"10.1126\/science.235.4792.1038","article-title":"Foam structures with a negative Poisson\u2019s ratio,","volume":"235","author":"Lakes","year":"1987","journal-title":"Science"},{"key":"key\n\t\t\t\t20180507100047_B2","doi-asserted-by":"crossref","first-page":"124","DOI":"10.1038\/353124a0","article-title":"Molecular network design,","volume":"353","author":"Evans","year":"1991","journal-title":"Nature"},{"key":"key\n\t\t\t\t20180507100047_B3","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1146\/annurev-matsci-070616-123908","article-title":"Harnessing instabilities to design tunable architected cellular materials,","volume":"47","author":"Bertoldi","year":"2017","journal-title":"Ann. Rev. Mater. Res."},{"key":"key\n\t\t\t\t20180507100047_B4","doi-asserted-by":"crossref","first-page":"105004","DOI":"10.1088\/0964-1726\/21\/10\/105004","article-title":"Comparative study of auxetic geometries by means of computer-aided design and engineering,","volume":"21","author":"Elipe","year":"2012","journal-title":"Smart Mater. Struct."},{"key":"key\n\t\t\t\t20180507100047_B5","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1038\/nmat3134","article-title":"Poisson\u2019s ratio and modern materials,","volume":"10","author":"Greaves","year":"2011","journal-title":"Nat. Mater."},{"key":"key\n\t\t\t\t20180507100047_B6","doi-asserted-by":"crossref","first-page":"8079","DOI":"10.1002\/adma.201601363","article-title":"Negative Poisson\u2019s ratio in modern functional materials,","volume":"28","author":"Huang","year":"2016","journal-title":"Adv. Mater."},{"key":"key\n\t\t\t\t20180507100047_B7","doi-asserted-by":"crossref","first-page":"5111","DOI":"10.1039\/C6RA27333E","article-title":"Auxetic mechanical metamaterials,","volume":"7","author":"Kolken","year":"2017","journal-title":"RSC Adv."},{"key":"key\n\t\t\t\t20180507100047_B8","doi-asserted-by":"crossref","first-page":"63","DOI":"10.1146\/annurev-matsci-070616-124118","article-title":"Negative-Poisson\u2019s-ratio materials: auxetic solids,","volume":"47","author":"Lakes","year":"2017","journal-title":"Ann. Rev. Mater. Res."},{"key":"key\n\t\t\t\t20180507100047_B9","doi-asserted-by":"crossref","first-page":"4782","DOI":"10.1002\/adma.201201644","article-title":"Micro-\/nanostructured mechanical metamaterials,","volume":"24","author":"Lee","year":"2012","journal-title":"Adv. Mater."},{"key":"key\n\t\t\t\t20180507100047_B10","doi-asserted-by":"crossref","first-page":"041101","DOI":"10.1063\/1.4964479","article-title":"Auxetic nanomaterials: recent progress and future development,","volume":"3","author":"Park","year":"2016","journal-title":"Appl. Phys. Rev."},{"key":"key\n\t\t\t\t20180507100047_B11","doi-asserted-by":"crossref","first-page":"1847","DOI":"10.1002\/adem.201600053","article-title":"Three decades of auxetics research: Materials with negative Poisson\u2019s ratio: A review,","volume":"18","author":"Saxena","year":"2016","journal-title":"Adv. Eng. Mater."},{"key":"key\n\t\t\t\t20180507100047_B12","doi-asserted-by":"crossref","first-page":"20150033","DOI":"10.1098\/rspa.2015.0033","article-title":"Geometric auxetics.","volume":"471","author":"Borcea","year":"2015","journal-title":"Proc. R. Soc. A"},{"key":"key\n\t\t\t\t20180507100047_B13","doi-asserted-by":"crossref","first-page":"2633","DOI":"10.1098\/rspa.2009.0676","article-title":"Periodic frameworks and flexibility","volume":"466","author":"Borcea","year":"2010","journal-title":"Proc. R. Soc. A"},{"key":"key\n\t\t\t\t20180507100047_B14","first-page":"1093","article-title":"Minimally rigid periodic graphs","volume":"43","author":"Borcea","year":"2011","journal-title":"Bull. Math. Soc."},{"key":"key\n\t\t\t\t20180507100047_B15","doi-asserted-by":"crossref","first-page":"20120143","DOI":"10.1098\/rsta.2012.0143","article-title":"Frameworks with crystallographic symmetry,","volume":"372","author":"Borcea","year":"2014","journal-title":"Phil. Trans. R. Soc. A"},{"key":"key\n\t\t\t\t20180507100047_B16","first-page":"371","article-title":"Deforming diamond","volume":"82","author":"Borcea","year":"2017","journal-title":"IMA J. Appl. Math."},{"key":"key\n\t\t\t\t20180507100047_B17","doi-asserted-by":"crossref","first-page":"747","DOI":"10.1007\/s00454-015-9689-7","article-title":"Liftings and stresses for planar periodic frameworks","volume":"53","author":"Borcea","year":"2015","journal-title":"Discrete Comput. Geom."},{"key":"key\n\t\t\t\t20180507100047_B18","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1007\/978-3-319-06698-1_41","article-title":"Kinematics of expansive planar periodic mechanisms,","volume-title":"Advances in Robot Kinematics (ARK\u201914)","author":"Borcea","year":"2014"},{"key":"key\n\t\t\t\t20180507100047_B19","doi-asserted-by":"crossref","first-page":"213","DOI":"10.2138\/am-1997-3-401","article-title":"Theory of displacive phase transitions in minerals","volume":"82","author":"Dove","year":"1997","journal-title":"Amer. Mineral."},{"key":"key\n\t\t\t\t20180507100047_B20","doi-asserted-by":"crossref","first-page":"1289","DOI":"10.1016\/0956-7151(94)90145-7","article-title":"Auxetic foams: Modeling negative Poisson\u2019s ratios.","volume":"42","author":"Evans","year":"1994","journal-title":"Acta Metall. Mater."},{"key":"key\n\t\t\t\t20180507100047_B21","doi-asserted-by":"crossref","first-page":"3121","DOI":"10.1098\/rspa.2011.0667","article-title":"Three-dimensional cellular structures with negative Poisson\u2019s ratio and negative compressibility properties,","volume":"468","author":"Grima","year":"2012","journal-title":"Proc. R. Soc. A"},{"key":"key\n\t\t\t\t20180507100047_B22","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijsolstr.2016.06.027","article-title":"Geometry: The leading parameter for the Poisson\u2019s ratio of bending-dominated cellular solids,","volume":"100\u2013101","author":"Mitschke","year":"2016","journal-title":"Int. J. Solids Struct."},{"key":"key\n\t\t\t\t20180507100047_B23","doi-asserted-by":"crossref","first-page":"17066","DOI":"10.1038\/natrevmats.2017.66","article-title":"Flexible mechanical metamaterials,","volume":"2","author":"Bertoldi","year":"2017","journal-title":"Nat. Rev. Mater."},{"key":"key\n\t\t\t\t20180507100047_B24","doi-asserted-by":"crossref","first-page":"25","DOI":"10.1016\/j.eml.2015.09.004","article-title":"Designer matter: A perspective,","volume":"5","author":"Reis","year":"2015","journal-title":"Extreme Mech. Lett."},{"key":"key\n\t\t\t\t20180507100047_B25","article-title":"Auxetic deformations and elliptic curves,","author":"Borcea","year":"2016"},{"key":"key\n\t\t\t\t20180507100047_B26","doi-asserted-by":"crossref","first-page":"442","DOI":"10.1137\/16M1088259","article-title":"New principles for auxetic periodic design,","volume":"1","author":"Borcea","year":"2017","journal-title":"SIAM J. Appl. Algebra Geom."},{"key":"key\n\t\t\t\t20180507100047_B27","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1098\/rspa.2011.0273","article-title":"On the auxetic properties of generic rotating rigid triangles,","volume":"468","author":"Grima","year":"2012","journal-title":"Proc. R. Soc. A"},{"key":"key\n\t\t\t\t20180507100047_B28","doi-asserted-by":"crossref","first-page":"1531","DOI":"10.1039\/b004305m","article-title":"Self expanding molecular networks,","volume":"16","author":"Grima","year":"2000","journal-title":"Chem. Commun."},{"key":"key\n\t\t\t\t20180507100047_B29","doi-asserted-by":"crossref","first-page":"12369","DOI":"10.1073\/pnas.1119941109","article-title":"Surface phonons, elastic response, and conformal invariance in twisted kagome lattices,","volume":"109","author":"Sun","year":"2012","journal-title":"Proc. Nat. Acad. Sci. U.S.A."},{"key":"key\n\t\t\t\t20180507100047_B30","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1016\/0167-6636(94)00069-7","article-title":"Tailoring materials with prescribed elastic properties,","volume":"20","author":"Sigmund","year":"1995","journal-title":"Mech. Mater."},{"key":"key\n\t\t\t\t20180507100047_B31","doi-asserted-by":"crossref","first-page":"56","DOI":"10.1016\/j.jmps.2016.02.010","article-title":"A class of auxetic three-dimensional lattices,","volume":"91","author":"Cabras","year":"2016","journal-title":"J. Mech. Phys. Solids"},{"key":"key\n\t\t\t\t20180507100047_B32","doi-asserted-by":"crossref","first-page":"3385","DOI":"10.1098\/rspa.2006.1726","article-title":"Poisson\u2019s ratio in cubic materials.","volume":"462","author":"Norris.","year":"2006","journal-title":"Proc. R. Soc. A"},{"key":"key\n\t\t\t\t20180507100047_B33","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1109\/84.585787","article-title":"Design and fabrication of compliant mechanisms and material structures with negative Poisson\u2019s ratio,","volume":"6","author":"Larsen","year":"1997","journal-title":"J. MicroElectroMech. Syst."},{"key":"key\n\t\t\t\t20180507100047_B34","doi-asserted-by":"crossref","first-page":"1105","DOI":"10.1016\/0022-5096(92)90063-8","article-title":"Composite materials with Poisson\u2019s ratio close to $-$1,","volume":"40","author":"Milton","year":"1992","journal-title":"J. Mech. Phys. Solids"}],"container-title":["The Quarterly Journal of Mechanics and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/academic.oup.com\/qjmam\/article-pdf\/71\/2\/125\/24794683\/hbx028.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,6]],"date-time":"2019-10-06T04:37:24Z","timestamp":1570336644000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/qjmam\/article\/71\/2\/125\/4727500"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,11]]},"references-count":34,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2017,12,11]]},"published-print":{"date-parts":[[2018,5,1]]}},"URL":"https:\/\/doi.org\/10.1093\/qjmam\/hbx028","relation":{},"ISSN":["0033-5614","1464-3855"],"issn-type":[{"value":"0033-5614","type":"print"},{"value":"1464-3855","type":"electronic"}],"subject":[],"published-other":{"date-parts":[[2018,5]]},"published":{"date-parts":[[2017,12,11]]}}}