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

Comments

Peer reviewed post-print.

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