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
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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