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

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.peer-reviewe

A novel mechanical metamaterial exhibiting auxetic behavior and negative compressibility

Auxetics (negative Poisson’s ratio) and materials with negative linear compressibility (NLC) exhibit the anomalous mechanical properties of getting wider rather than thinner when stretched and expanding in at least one direction under hydrostatic pressure, respectively. A novel mechanism—termed the ‘triangular elongation mechanism’—leading to such anomalous behavior is presented and discussed through an analytical model. Amongst other things, it is shown that this novel mechanism, when combined with the well-known ‘rotating squares’ model, can generate giant negative Poisson’s ratios when the system is stretched.peer-reviewe

Auxetic-inspired honeycomb macrostructures with anomalous tailormade thermal expansion properties including “negative” heat-shrinking characteristics

Negative thermal expansion (NTE) materials and structures exhibit the anomalous property of shrinking rather than expanding when heated. This work examines the potential of multimaterial planar re-entrant and non-re-entrant honeycombs to exhibit anomalous thermal expansion properties. Expressions for the coefficient of thermal expansion as a function of the geometric parameters and intrinsic thermal expansion properties were derived for any in-plane direction. It was shown that re-entrant honeycombs, a metamaterial which is well known for its auxetic characteristics, can be made to exhibit NTE in specific directions when constructed from conventional positive thermal expansion (PTE) materials, provided that the slanting ligaments expand more than the vertical ligaments when heated and that the geometry is amenable. Conversely, it was shown that the construction of such honeycombs from NTE components will not necessarily result in a system which exhibits NTE in all directions. Furthermore, conditions which result in honeycombs demonstrating zero thermal expansion (ZTE) coefficients in specific directions were also explored.peer-reviewe

The multidirectional auxeticity and negative linear compressibility of a 3D mechanical metamaterial

In this work, through the use of a theoretical model, we analyse the potential of a specific three-dimensional mechanical metamaterial composed of arrowhead-like structural units to exhibit a negative Poisson’s ratio for an arbitrary loading direction. Said analysis allows us to assess its suitability for use in applications where materials must be able to respond in a desired manner to a stimulus applied in multiple directions. As a result of our studies, we show that the analysed system is capable of exhibiting auxetic behaviour for a broad range of loading directions, with isotropic behaviour being shown in some planes. In addition to that, we show that there are also certain loading directions in which the system manifests negative linear compressibility. This enhances its versatility and suitability for a number of applications where materials exhibiting auxetic behaviour or negative linear compressibility are normally implemented.peer-reviewe