Perforated Sheets Exhibiting Negative Poisson's Ratios

Abstract

Sheets made from readily available conventional materials containing diamond or star shaped perforations are shown to exhibit various Poisson's ratio values which could also be negative (auxetic). This behavior may be exhibited in both tension and compression and can be explained through models based on “rotating rigid units.” This provides an easy manner for the manufacture of auxetic or conventional systems at any scale which can be tailor made to exhibit particular values of the Poisson's ratio.

Low Porosity Metallic Periodic Structures with Negative Poisson's Ratio

“…For the circular void sample, the deformation mechanism is stretching much the same as a similar void-less structure would be. By contrast, as perviously shown in the analytical study by Grima and Gatt [27], the deformation mechanism in the elliptical void sample is mostly due to rotation, leading to a negative Poisson's ratio. Finally, the completely different mechanism by which the two structures carry the load results in very different stress distributions within the material, as shown in Fig.…”

“…The design of 2-D systems capable of retaining a negative Poisson's ratio at such low values of porosity still remains a challenge [26]. Although it has been recently shown through an analytical/numerical study that diamond or star shaped perforations introduced in thin sheets can lead to auxetic behavior [27], convincing experimental evidence of a low porosity auxetic material has not been reported. The goal of this work is to demonstrate one such low porosity structure in metal via numerical simulation and material testing.…”

Auxetic behaviour from connected different-sized squares and rectangles

“…For example, a direct application of this work would be as a template for the design and manufacture of perforated sheets, which exhibit NPR in analogy to the recent work based on squares (Grima & Gatt 2010). On a microlevel, microstructures based on these models can be micromachined using techniques such as laser ablation and mechanical micromachining.…”

Auxetic behaviour in non-crystalline materials having star or triangular shaped perforations

“…Although these systems are limited due to the fact that they only exhibit Poisson's ratio in compression, they offer the advantage that they may be manufactured rather easily [46] which overcome the current limitation that most auxetics discovered so far are difficult or expensive to manufacture on a large scale. Gatt and Grima [47,48] have also recently proposed that auxetic behaviour may be obtained in both tension and compression if readily available conventional sheets of material are perforated with particular shapes in such a way that the resulting pattern's characteristics resemble known auxetic models. In particular, they have shown that rubber sheets having diamond or paralellogramic-shaped perforations can simulate the well known "rotating squares" [32] or "rotating rectangles" [36] models to achieve various values of the Poisson's ratio which can also be negative.…”