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Soc. open sci."],"published-print":{"date-parts":[[2022,8]]},"abstract":"<jats:p>The auxetic structures considered in this paper are three-dimensional periodic bar-and-joint frameworks. We start with the specific purpose of obtaining an auxetic design with underlying periodic graph of low valency. Adapting a general methodology, we produce an initial framework with valency seven and one degree of freedom. Then, we describe a saturation process, whereby edge orbits are added up to valency 16, with no alteration of the deformation path. This is reflected in a large dimension for the space of periodic self-stresses. The saturated version has higher crystallographic symmetry and allows a precise description of the deformation trajectory. Reducing saturation by adequate removal of edge orbits results in vast numbers of distinct auxetic designs which obey the same kinematics.<\/jats:p>","DOI":"10.1098\/rsos.220765","type":"journal-article","created":{"date-parts":[[2022,8,31]],"date-time":"2022-08-31T07:06:35Z","timestamp":1661929595000},"update-policy":"https:\/\/doi.org\/10.1098\/crossmark-policy","source":"Crossref","is-referenced-by-count":0,"title":["Saturation and periodic self-stress in geometric auxetics"],"prefix":"10.1098","volume":"9","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6207-9127","authenticated-orcid":true,"given":"Ciprian S.","family":"Borcea","sequence":"first","affiliation":[{"name":"Department of Mathematics, Rider University, Lawrenceville, NJ, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ileana","family":"Streinu","sequence":"additional","affiliation":[{"name":"Department of Computer Science Smith College, Northampton, MA, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"175","published-online":{"date-parts":[[2022,8,31]]},"reference":[{"key":"e_1_3_5_2_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2009.0676"},{"key":"e_1_3_5_3_2","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2015.0033"},{"key":"e_1_3_5_4_2","doi-asserted-by":"publisher","DOI":"10.1093\/qjmam\/hbx028"},{"key":"e_1_3_5_5_2","unstructured":"Norton RL. 1992 Design of machinery: an introduction to the synthesis and analysis of mechanisms and machines . 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