Saturation and periodic self-stress in geometric auxetics
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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The Royal Society
2022-08-01
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| Series: | Royal Society Open Science |
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| Online Access: | https://royalsocietypublishing.org/doi/10.1098/rsos.220765 |
| _version_ | 1827960582114902016 |
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| author | Ciprian S. Borcea Ileana Streinu |
| author_facet | Ciprian S. Borcea Ileana Streinu |
| author_sort | Ciprian S. Borcea |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-09T16:12:03Z |
| format | Article |
| id | doaj.art-3645f67f44b749e189e20347813acc28 |
| institution | Directory Open Access Journal |
| issn | 2054-5703 |
| language | English |
| last_indexed | 2024-04-09T16:12:03Z |
| publishDate | 2022-08-01 |
| publisher | The Royal Society |
| record_format | Article |
| series | Royal Society Open Science |
| spelling | doaj.art-3645f67f44b749e189e20347813acc282023-04-24T09:17:22ZengThe Royal SocietyRoyal Society Open Science2054-57032022-08-019810.1098/rsos.220765Saturation and periodic self-stress in geometric auxeticsCiprian S. Borcea0Ileana Streinu1Department of Mathematics, Rider University, Lawrenceville, NJ, USADepartment of Computer Science Smith College, Northampton, MA, USAThe 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.https://royalsocietypublishing.org/doi/10.1098/rsos.220765periodic frameworkauxetic deformationself-stressmatroid basis polytopecognate frameworks |
| spellingShingle | Ciprian S. Borcea Ileana Streinu Saturation and periodic self-stress in geometric auxetics Royal Society Open Science periodic framework auxetic deformation self-stress matroid basis polytope cognate frameworks |
| title | Saturation and periodic self-stress in geometric auxetics |
| title_full | Saturation and periodic self-stress in geometric auxetics |
| title_fullStr | Saturation and periodic self-stress in geometric auxetics |
| title_full_unstemmed | Saturation and periodic self-stress in geometric auxetics |
| title_short | Saturation and periodic self-stress in geometric auxetics |
| title_sort | saturation and periodic self stress in geometric auxetics |
| topic | periodic framework auxetic deformation self-stress matroid basis polytope cognate frameworks |
| url | https://royalsocietypublishing.org/doi/10.1098/rsos.220765 |
| work_keys_str_mv | AT cipriansborcea saturationandperiodicselfstressingeometricauxetics AT ileanastreinu saturationandperiodicselfstressingeometricauxetics |