Auxetic behaviour from connected different-sized squares and rectangles

Auxetic materials exhibit the unusual property of becoming fatter when uniaxially stretched and thinner when uniaxially compressed (i.e. they exhibit a negative Poisson ratio; NPR), a property that may result in various enhanced properties. The NPR is the result of the manner in which particular geometric features in the micro- or nanostructure of the materials deform when they are subjected to uniaxial loads. Here, we propose and discuss a new model made from different-sized rigid rectangles, which rotate relative to each other. This new model has the advantage over existing models that it can be used to describe the properties of very different systems ranging from silicates and zeolites to liquid-crystalline polymers. We show that such systems can exhibit scale-independent auxetic behaviour for stretching in particular directions, with Poisson’s ratios being dependent on the shape and relative size of different rectangles in the model and the angle between them.peer-reviewe

Composites with needle-like inclusions exhibiting negative thermal expansion : a preliminary investigation

In this work a simple cylindrical structure with a stiff needle-like inclusion embedded within a much softer matrix is presented and analysed with the aim of obtaining a system with tunable thermal expansion properties. It is shown that by the correct combination of the thermal and mechanical properties of the matrix and inclusion, it is possible to design a system which can be tailor-made to exhibit particular values of the coefficient of thermal expansion (CTE) in the radial direction and also negative thermal expansion (NTE). In particular an analytical model to quantify the radial strain with changes in temperature is derived and verified through finite element analysis. The model is used to find correct property combinations which lead to particular values of thermal expansion which could also be negative or zero.peer-reviewe

Maximizing negative thermal expansion via rigid unit modes : a geometry-based approach

Existent rigid unit mode (RUM) models based on rotating squares, which may explain the phenomenon of negative thermal expansion (NTE), are generalized so as to assess the NTE potential for novel systems made from rectangular or rhombic rigid units. Analytical models for the area coefficients of thermal expansion (CTE) of these innovative networks are derived in an attempt to determine the optimal geometrical parameters and connectivity for maximum NTE. It was found that all systems exhibit NTE, the extent of which is determined by the shape and connectivity of the elemental rigid units (side lengths ratio or internal angle). It was also found that some of the networks proposed here should exhibit significantly superior NTE properties when compared with the well-known network of squares, and that for optimal NTE characteristics, pencil-like rigid units should be used rather than square-shaped ones, as these permit larger pore sizes that are more conducive to NTE. All this compliments earlier work on the negative Poisson's ratio (auxetic) potential of such systems and may provide a route for the design of new materials exhibiting superior thermo-mechanical characteristics including specifically tailored CTEs or giant NTE characteristics.peer-reviewe

On the mechanical properties and auxetic potential of various organic networked polymers

We simulate and analyse three types of two-dimensional networked polymers which have been predicted to exhibit on-axis auxetic behaviour (negative Poisson's ratio), namely (1) polyphenylacetylene networks that behave like flexing re-entrant honeycombs, commonly referred to as ‘reflexynes’, (2) polyphenylacetylene networks that mimic the behaviour of rotating triangles, commonly referred to as ‘polytriangles’ and (3) networked polymers built from calix[4]arene units. More specifically, we compute and compare their in-plane off-axis mechanical behaviour, in particular their off-axis Poisson's ratios and show that in some cases, the sign and magnitude of the Poisson's ratio are dependent on the direction of loading. We propose two functions that can provide a measure for the extent of auxeticity for such anisotropic materials and show that the polytriangles are predicted as the most auxetic when compared with the other networks with the reflexyne re-entrant networks being the least auxetic.peer-reviewe

Hexagonal honeycombs with zero Poisson's ratios and enhanced stiffness

In view of their potential applications in sandwich structures, there has been increasing interest in honeycomb networks. Several different types of honeycomb systems have been proposed each exhibiting different mechanical properties. Here we propose a new hexagonal honeycomb structure composed of two different geometrical features: a re-entrant feature which is known to generate auxetic behavior, and a non re-entrant feature found in regular hexagonal honeycombs which leads to conventional behavior. This results in a “semi re-entrant honeycomb” built of alternate conventional and auxetic layers. Finite element analysis and analytical modeling of these honeycombs show that they exhibit a zero Poisson ratio in one direction and a higher than normal Young's modulus in the orthogonal direction. We also show that by virtue of its zero Poisson's ratio, this honeycomb has a natural tendency to form cylindrical shaped curvatures, something which is very difficult to achieve with conventional or auxetic honeycombs.peer-reviewe

Core-shell modelling of auxetic inorganic materials

This paper investigates the suitability of the General Utility Lattice Program (GULP) for studying auxetic materials at the molecular level. GULP is a force-field based molec- ular modelling package which incorporates the ‘core-shell’ model for simulating polarisability. A validation procedure was performed where the capability of GULP to reproduce the structural and mechanical properties of SOD (a zeolite for which the single crystalline elastic constants have been experimentally measured). It was found that not all GULP libraries (force-fields) could reproduce these properties, although the ‘Catlow 1992’ and ‘Sauer 1997’ libraries were found the produce good results. These libraries were then used to study the all-silica forms of various ‘presumably auxetic’ zeolites. The simulations generally confirmed the conclusions re- ported in earlier studies, and in particular, the fibrous zeolites THO, NAT and EDI where once again shown to be auxetic in the (001) plane. A study was also performed aimed at assessing the effect of interstitial species on the mechanical properties of NAT where it was shown that these species reduce the auxetic effect. This is very significant as once again we have confirmed the potential of these materials as molecular level auxetics, and hopefully, these results will result in generating more interest into the fascinating materials which could be used in many practical applications (e.g. tuneable molecular sieves).peer-reviewe

On the auxetic properties of generic rotating rigid triangles

Materials having a negative Poisson’s 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 Poisson’s 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 Poisson’s ratios, are also discussed.peer-reviewe

Simulations of the properties of elongated hexagonal dodecahedron systems

This study considers a 3D basic unit-cell proposed for auxetic and non-auxetic foams namely the elongated hexagonal dodecahedron deforming through changes in angle between its ligaments (idealised hinging model). This structure was studied in detail for the potential of exhibiting negative Poisson’s ratio and/or negative compressibility by means of a method based on standard force-field molecular modelling technique, termed as Empirical Modelling Using Dummy Atoms (EMUDA). The mechanical properties obtained from this method were then compared to a previously published analytical model of this structure [Grima J N, Caruana-Gauci R, Attard D, and Gatt R 2012, Proc. Roy. Soc. A 468 3121], and found to be in good agreement with each other. The results showed that this system can exhibit zero Poisson’s ratios in one of its planes and positive or negative Poisson’s ratios in other planes, depending on the geometry of the model. It was also shown that under certain conditions, negative linear and/or area compressibility was also exhibited.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

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