New principles for auxetic periodic design

TL;DR

This paper demonstrates that in any dimension two or higher, there are infinitely many possible designs for periodic frameworks with auxetic properties, using a geometric deformation approach.

Contribution

It introduces a geometric method to classify and generate an infinite variety of auxetic periodic framework designs across dimensions.

Findings

Infinite range of auxetic designs in any dimension ≥ 2

Development of a geometric approach to auxetic deformation trajectories

Frameworks exhibit diverse auxetic behaviors based on geometric principles

Abstract

We show that, for any given dimension $d\geq 2$, the range of distinct possible designs for periodic frameworks with auxetic capabilities is infinite. We rely on a purely geometric approach to auxetic trajectories developed within our general theory of deformations of periodic frameworks.