Periodic auxetics: Structure and design

TL;DR

This paper introduces a geometric framework for designing periodic auxetic materials, revealing essential convexity properties that enable systematic creation of auxetic structures with negative Poisson's ratio.

Contribution

It establishes a geometric approach to identify and generate periodic auxetic structures, moving beyond the traditional focus on cellular structures and negative Poisson's ratio.

Findings

Geometric approach effectively characterizes auxetic deformations.

Convexity properties via homothetic ellipsoids are key to auxetic behavior.

Systematic generation of infinite auxetic designs is possible.

Abstract

Materials science has adopted the term of auxetic behavior for structural deformations where stretching in some direction entails lateral widening, rather than lateral shrinking. Most studies, in the last three decades, have explored repetitive or cellular structures and used the notion of negative Poisson's ratio as the hallmark of auxetic behavior. However, no general auxetic principle has been established from this perspective. In the present paper, we show that a purely geometric approach to periodic auxetics is apt to identify essential characteristics of frameworks with auxetic deformations and can generate a systematic and endless series of periodic auxetic designs. The critical features refer to convexity properties expressed through families of homothetic ellipsoids.