TL;DR
This paper develops a geometric mathematical framework to analyze and predict auxetic behavior in structures across any dimension, enabling the design of new auxetic mechanisms without experimental testing.
Contribution
It introduces a purely geometric theory based on one-parameter deformations of periodic frameworks, offering new principles for auxetic design and expanding the catalog of known auxetic structures.
Findings
Successfully predicts auxetic capabilities of known structures
Proposes new principles for auxetic design
Provides infinite planar auxetic mechanisms and new 3D structures
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.
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