Realizations of isostatic material frameworks
Abstract
This article studies the set of equivalent realizations of isostatic frameworks and algorithms for finding all such realizations. It is shown that an isostatic framework has an even number of equivalent realizations that preserve edge lengths and connectivity. The complete set of equivalent realizations for a toy framework with pinned boundary in two dimensions is enumerated and the impact of boundary length on the emergence of these realizations is studied. To ameliorate the computational complexity of finding a solution to a large multivariate quadratic system corresponding to the constraints, alternative methods—based on constraint reduction and distance-based covering map or Cayley parameterization of the search space—are presented. The application of these methods is studied on atomic clusters, a model of 2D glasses and jamming.
Citation
Sadjadi , M , Hagh , V F , Kang , M , Sitharam , M , Connelly , R , Gortler , S J , Theran , L , Holmes-Cerfon , M & Thorpe , M F 2021 , ' Realizations of isostatic material frameworks ' , Physica Status Solidi. B , vol. 258 , no. 9 , 2000555 . https://doi.org/10.1002/pssb.202000555
Publication
Physica Status Solidi. B
Status
Peer reviewed
ISSN
0370-1972Type
Journal article
Rights
Copyright © 2021 Wiley-VCH GmbH. This work has been made available online in accordance with publisher policies or with permission. Permission for further reuse of this content should be sought from the publisher or the rights holder. This is the author created accepted manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at https://doi.org/10.1002/pssb.202000555
Description
The authors would like to thank financial support though NSF grant no. DMS 1564468 (Connelly, Gortler, Holmes‐Cerfon, Sitharam, Thorpe).Collections
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