Theory of strains in auxetic materials

TL;DR

This paper develops a first-principles model for strains in disordered auxetic materials, revealing how internal structural elements called auxetons govern auxetic behavior through stress-induced rotations and expansions.

Contribution

It introduces a novel explicit expression for strains in disordered auxetic structures based on internal auxeton dynamics, extending beyond traditional elasticity theory.

Findings

Explicit dependence of strain rate on local structure

Identification of auxeton rotation and expansion mechanisms

Model applicable to any auxeton-based disordered system

Abstract

Auxetic materials, or negative-Poisson's-ratio materials, are important technologically and fascinating theoretically. When loaded by external stresses, their internal strains are governed by correlated motion of internal structural degrees of freedom. The modelling of such materials is mainly based on ordered structures, despite existence of auxetic behaviour in disordered structures and the advantage in manufacturing disordered structures for most applications. We describe here a first-principles expression for strains in disordered such materials, based on insight from a family of 'iso-auxetic' structures. These are structures, consisting of internal structural elements, which we name 'auxetons', whose inter-element forces can be computed from statics alone. Iso-auxetic structures make it possible not only to identify the mechanisms that give rise to auxeticity, but also to write down the explicit dependence of the strain rate on the local structure, which is valid to all auxetic materials. It is argued that stresses give rise to strains via two mechanisms: auxeton rotations and auxeton expansion / contraction. The former depends on the stress via a local fabric tensor, which we define explicitly for 2D systems. The latter depends on the stress via an expansion tensor. Whether a material exhibits auxetic behaviour or not depends on the interplay between these two fields. This description has two major advantages: it applies to any auxeton-based system, however disordered, and it goes beyond conventional elasticity theory, providing an explicit expression for general auxetic strains and outlining the relevant equations.