Ruben Gatt

Tailoring Graphene to Achieve Negative Poisson's Ratio Properties

Graphene can be made auxetic through the introduction of vacancy defects. This results in the thinnest negative Poissons ratio material at ambient conditions known so far, an effect achieved via a nanoscale de-wrinkling mechanism that mimics the behavior at the macroscale exhibited by a crumpled sheet of paper when stretched.

Hierarchical Auxetic Mechanical Metamaterials

Auxetic mechanical metamaterials are engineered systems that exhibit the unusual macroscopic property of a negative Poissons ratio due to sub-unit structure rather than chemical composition. Although their unique behaviour makes them superior to conventional materials in many practical applications, they are limited in availability. Here, we propose a new class of hierarchical auxetics based on the rotating rigid units mechanism. These systems retain the enhanced properties from having a negative Poissons ratio with the added benefits of being a hierarchical system. Using simulations on typical hierarchical multi-level rotating squares, we show that, through design, one can control the extent of auxeticity, degree of aperture and size of the different pores in the system. This makes the system more versatile than similar non-hierarchical ones, making them promising candidates for industrial and biomedical applications, such as stents and skin grafts.

On the potential of connected stars as auxetic systems

Auxetic materials and structures exhibit the unexpected behaviour of getting wider when stretched and thinner when compressed. This behaviour requires the structures (the internal structure in the case of materials) to have geometric features, which must deform in a way that results in the structure expanding when stretched. This paper assesses the potential for auxetic behaviour of a novel class of two-dimensional periodic structures which can be described as “connected stars” as they contain star-shaped units of different rotational symmetry which are connected together to form two-dimensional periodic structures. These structures will be studied through a technique based on force-field based methods (the EMUDA technique) and it will be shown that some, but not all, of these structures can exhibit auxetic behaviour. An attempt is made to explain the reasons for the presence or absence of a negative Poissons ratio in these systems.

Natrolite: A zeolite with negative Poisson’s ratios

The recently published experimental elastic constants [C. Sanchez-Valle, S. V. Sinogeikin, Z. A. Lethbridge, R. I. Walton, C. W. Smith, K. E. Evans, and J. D. Bass, J. Appl. Phys. 98, 053508 (2005)] for single crystals of the orthorhombic aluminosilicate zeolite NAT (natrolite, Na2(Al2Si3O10)2H2O, Fdd2) throw valuable light on the potential of NAT as a material which exhibits single crystalline negative Poisson’s ratios (auxetic). On performing an off-axis analysis of these elastic constants we confirm that the zeolite natrolite exhibits auxetic behavior in the (001) plane. This supports our preliminary report that NAT-type zeolites exhibit auxetic behavior through a mechanism involving microscopic rotation of semi-rigid structural units.

Smart metamaterials with tunable auxetic and other properties

Auxetic and other mechanical metamaterials are typically studied in situations where they are subjected solely to mechanical forces or displacements even though they may be designed to exhibit additional anomalous behaviour or tunability when subjected to other disturbances such as changes in temperature or magnetic fields. It is shown that externally applied magnetic fields can tune the geometry and macroscopic properties of known auxetics that incorporate magnetic component/s, thus resulting in a change of their macroscopic properties. Anomalous properties which are observed in such novel magneto-mechanical systems include tunable Poisson’s ratios, bi-stability or multi-stability, depending on the applied magnetic fields, and other electromagnetic‐mechanical effects such as strain dependent induced electric currents and magnetic fields. The properties exhibited depend, amongst other things, on the relative position and orientation of the magnetic insertion/s within the structure, the geometry of the system and the magnetic strength of the magnetic components, including that of the external magnetic field.

On the origin of auxetic behaviour in the silicate α-cristobalite

The experimentally observed negative Poissons ratios in the silicate α-cristobalite are explained through a two-dimensional ‘rotation of rigid units’ model involving ‘rotating rectangles’ hence providing a new insight into the way nature can achieve this unusual property.

Three-dimensional cellular structures with negative Poisson's ratio and negative compressibility properties

A three-dimensional cellular system that may be made to exhibit some very unusual but highly useful mechanical properties, including negative Poissons ratio (auxetic), zero Poissons ratio, negative linear and negative area compressibility, is proposed and discussed. It is shown that such behaviour is scale-independent and may be obtained from particular conformations of this highly versatile system. This model may be used to explain the auxetic behaviour in auxetic foams and in other related cellular systems; such materials are widely known for their superior performance in various practical applications. It may also be used as a blueprint for the design and manufacture of new man-made multifunctional systems, including auxetic and negative compressibility systems, which can be made to have tailor-made mechanical properties.

On the Auxetic Properties of 'Rotating Rectangles' with Different Connectivity

Auxetic materials and structures exhibit the unusual property of becoming wider when stretched and thinner when compressed, i.e., they have negative Poisson’s ratios. In recent years, this unusual behaviour has been predicted or experimentally measured in a number of naturally-occurring and man-made materials ranging from foams where the auxetic effect arises from the particular microstructure of the foams to silicates and zeolites where the auxetic behaviour occurs at themolecular level. In these auxetic systems, the negative Poisson’s ratios can be explained in terms of models based on the geometry of the system (i.e., the geometry of the material’s internal structure) and the way this geometry changes as a result of applied loads (deformationmechanism). In recent years various two and three dimensional theoretical models and structures which can lead to negative Poisson’s ratio have been proposed including, two and threedimensional ‘re-entrant’ systems, models based on rigid ‘free’ molecules, chiral structures and systems made from ‘rotating rigid units’ such as squares, triangles, rectangles or tetrahdera. In all of these systems, the Poisson’s ratio does not depend on scale although it can depend on the relative dimensions of certain features in the geometry. In particular we have recently shown that whilst a two-dimensional system constructed from perfectly rigid squares connected together through simple hinges at the vertices of the squares will always maintain its aspect ratio when stretched or compressed [see Fig. 1(a)], i.e., it will exhibit constant Poisson’s ratios equal to 1 irrespective of the size of the square or direction of loading, the equivalent structure built from hinged rigid rectangles as illustrated in Fig. 1(b) will exhibit in-plane Poisson’s ratios which depend on the shape of the rectangles (the ratio of the lengths of the two sides) and the relative orientation of the rectangles (i.e., the angles that two adjacent rectangles make with respect to each other). This means that for such a system, the Poisson’s ratios will be strain dependent and dependent on the direction of loading. This note is aimed at highlighting the fact that there exist two types of ‘rotating rectangles’ structures, and that two systems based on the same ‘building block’ (rigid rectangle) and same deformation mechanism (rectangle rotation), but different connectivity, exhibit very different mechanical properties. More specifically, for rectangles of the same size (a b), tessellating corner-sharing rectangular networks in which each corner is shared between two rectangles can only be formed from two connectivity schemes, which we shall refer to as Type I and Type II. The Type I network refers to the system where four rectangles are connected in such a way that the empty spaces between the rectangles form rhombi of size (a a) and (b b) as illustrated in Fig. 1(b). The Type II network refers to the system with a connectivity where the empty spaces between the rectangles form parallelograms of size (a b) as illustrated in Fig. 1(c). If the four rectangles are connected in any other way (for example, with the empty spaces between the rectangles forming a ‘kite’ of side lengths ‘a, a, b, b’) the resulting unit cannot form a tessellating structure. The Type I ‘rotating rectangles’ structure has been extensively studied and it has been shown that this structure exhibits properties which are dependent on the shape and size of the rectangles and are strain dependent and anisotropic. In particular it has been shown that such Type I ‘rotating rectangles’ structures are capable of exhibiting both positive and negative Poisson’s ratio where, for example, the on-axis Poisson’s ratios are dependent on the ratio of the lengths (a=b) and on the angle between the rectangles since: v21 1⁄4 ðv12Þ 1 1⁄4 a sin 2 ð Þ b cos 2 ð Þ a2 cos2 2 ð Þ b2 sin 2 ð Þ Here we study, for the first time, the behaviour of the Type II ‘rotating rectangles’ which as we will show exhibits very different properties. As illustrated in Fig. 1(c), a rectangular unit cell with cell sides are parallel to the Ox1 and Ox2 axis may be used to describe the Type II network. This unit cell contains two (a b) rectangles with projections in the Oxi directions given by:

On the auxetic properties of generic rotating rigid triangles

Materials having a negative Poissons ratio (auxetic) get fatter rather than thinner when uniaxially stretched. This phenomenon has been often explained through models that describe how particular geometric features in the micro or nanostructure of the material deform when subjected to uniaxial loads. Here, a new model based on scalene rigid triangles rotate relative to each other will be presented and analysed. It is shown that this model can afford a very wide range of Poissons ratio values, the sign and magnitude of which depends on the shape of the triangles and the angles between them. This new model has the advantage that it is very generic and may be potentially used to describe the properties in various types of materials, including auxetic foams and their relative surface density. Specific applications of this model, such as a blueprint for a system that can exhibit temperature-dependent Poissons ratios, are also discussed.

A system with adjustable positive or negative thermal expansion

We analyse the anisotropic thermal expansion properties of a two-dimensional structurally rigid construct made from rods of different materials connected together through hinges to form triangular units. In particular, we show that this system may be made to exhibit negative thermal expansion coefficients along certain directions or thermal expansion coefficients that are even more positive than any of the component materials. The end product is a multifunctional system with tunable thermal properties that can be tailor-made for particular practical applications.