The extent of deformations that a material undergoes when it is uniaxially stretched or compressed are quantified through the Poisson’s ratio, a property which is positive for most conventional materials. However, it is well known that Poisson’s ratio need not be always positive and the classical theory of elasticity suggests that the Poisson’s ratio of isotropic materials can assume values within the range of -1 to 0.5. The range is even wider for orthotropic and anisotropic materials.

Negative (or auxetic) Poisson’s ratios have now been discovered or introduced in a wide range of naturally occurring or man-made materials including foams, polymers, metals, silicates, and zeolites. Furthermore, various model structures and mechanisms which exhibit negative Poisson’s ratio have been proposed. These materials and structures have been shown to exhibit several enhanced macroscopic properties ranging from enhanced resistance to indentation to smart filtration or increased vibration and acoustic absorption properties.

Unfortunately, despite of all these developments, the availability of materials and structures which exhibit negative Poisson’s ratios is still very limited. Most auxetics discovered so far are difficult or expensive to manufacture on a large scale; only exhibit negative Poisson’s ratio for stretching in very particular directions and/or only exhibit negative Poisson’s ratio in compression.

At the University of Malta, Professor Joseph N. Grima and Ruben Gatt proposed a method to overcome these problems by suggesting novel auxetic systems. Their idea was to introduce perforations of particular shapes like diamond or star-shaped in sheets of conventional materials such as rubber. To verify their hypothesis, Grima and Gatt performed finite element (FE) simulations of cuboidal sheets made from an isotropic material in which they had introduced rhombic shaped perforations in a regular fashion. These arrangements were chosen in view of the similarities with other auxetic structures based on rotating rigid units which they had developed.

Four sets of simulations were performed with specimens of perforated sheets with diamond-shaped inclusions with different orientations, diamond-shaped inclusions of two different sizes and a sheet with star-shaped inclusions.



The results of these simulations in tension clearly suggest that these systems can exhibit a wide range of Poisson’s ratio which may be positive, negative, or zero. “In some cases, the predicted positive values of the Poisson’s ratio significantly exceed the magnitude of the Poisson’s ratio of material used. Similar properties where observed in compression,” Professor Grima concluded. “Our work suggests that systems based on the ideas proposed here can be designed to operate in both tension and compression and can be cheaply manufactured from readily available conventional sheets of material by simply introducing perforations of the appropriate shape placed in the right places. What is also very interesting is that what we are reporting here is a scale-independent effect and may be implemented at any lengthscale including the macro or millimetre scale but also the microscale by introducing micro-perforations. If adequately developed, this work could easily lead to the mass production of auxetic materials”.

J. N. Grima et al., Adv. Eng. Mater ; DOI: 10.1002/adem.201000005