Document Type
Article
Publication Date
12-23-2015
Publication Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Abstract
We formulate a mathematical theory of auxetic behavior based on one-parameter deformations of periodic frameworks. Our approach is purely geometric, relies on the evolution of the periodicity lattice and works in any dimension. We demonstrate its usefulness by predicting or recognizing, without experiment, computer simulations or numerical approximations, the auxetic capabilities of several well-known structures available in the literature. We propose new principles of auxetic design and rely on the stronger notion of expansive behavior to provide an infinite supply of planar auxetic mechanisms and several new three-dimensional structures.
Keywords
periodic framework, auxetic deformation, contraction operator, positive semidefinite cone, spectrahedron
Volume
471
Issue
2184
DOI
dx.doi.org/10.1098/rspa.2015.0033
ISSN
1471-2946
Recommended Citation
Borcea, Ciprian and Streinu, Ileana, "Geometric Auxetics" (2015). Computer Science: Faculty Publications, Smith College, Northampton, MA.
https://scholarworks.smith.edu/csc_facpubs/3
Open Access Policy Opt-Out
1
Comments
Peer reviewed accepted manuscript.