Mathematical modeling of auxetic systems: bridging the gap between analytical models and observation

Abstract

The Poisson’s ratio, a property which quantifies the changes in thickness when a material is stretched and compressed, can be determined as the negative of the transverse strain over the applied strain. In the scientific literature, there are various ways how strain may be defined and the actual definition used could result in a different Poisson’s ratio being computed. This paper will look in more detail at this by comparing the more commonly used forms of strain and the Poisson’s ratio that is computable from them. More specifically, an attempt is made to assess through examples on the usefulness of the various formulations to properly describe what can actually be observed, thus providing a clearer picture of which form of Poisson’s ratio should be used in analytical modelling.