Joseph N. Grima

Auxetic behavior from rotating squares

Auxetic materials exhibit the very unusual properties of becoming wider when stretched and narrower when squashed [1], that is they have negative Poisson’s ratios. Apart from the pure scientific interest of having materials showing such an unconventional property, a negative Poisson’s ratio gives a material several other beneficial effects such as an increased shear stiffness, an increased plane strain fracture toughness and an increased indentation resistance. These properties make auxetics superior to conventional materials for many practical applications [1, 2]. In recent years several auxetics have been fabricated by modifying the microstructure of existing materials, including foams [2] and microporous polymers [3]. A number of molecular auxetics have also been proposed [4–9] one example being α-cristobalite [7]. The auxetic behavior in these materials can be explained in terms of their geometry and deformation mechanism. Thus, the hunt for new auxetic materials is frequently approached through searching for geometric features which may give such behavior [9, 10]. In this letter we present a new mechanism to achieve a negative Poisson’s ratio. This is based on an arrangement involving rigid squares connected together at their vertices by hinges as illustrated in Fig. 1. This may be viewed as a two dimensional arrangement of squares or as a projection of a particular plane of a three dimensional structure. This latter type of geometry is commonly found in inorganic crystalline materials [8, 9, 11]. Referring to Fig. 1, for squares of side length “l” at an angle θ to each other, the dimensions of the unit cell in the Oxi directions are given by:

A novel mechanism for generating auxetic behaviour in reticulated foams: missing rib foam model

Abstract Foams have previously been fabricated with a negative Poissons ratio (termed auxetic foams). A novel model is proposed to explain this and to describe the strain-dependent Poissons function behaviour of honeycomb and foam materials. The model is two-dimensional and is based upon the observation of broken cell ribs in foams processed via the compression and heating technique usually employed to convert conventional foams to auxetic behaviour. The model has two forms: the “intact” form is a network of ribs with biaxial symmetry, and the “auxetic” form is a similar network but with a proportion of cell ribs removed. The model output is compared with that of an existing two-dimensional model and experimental data, and is found to be superior in predicting the Poissons function and marginally better at predicting the stress–strain behaviour of the experimental data than the existing model, using realistic values for geometric parameters.

Do Zeolites Have Negative Poisson's Ratios?

Consequently, the size of the resulting nanoparticles matches the dimension of the nanometer-sized cavities inside these swollen domains. The possibility of controlling the growth of the metal nanoclusters by changing the morphological features of the support represents a unique feature of resin supports, in which the metal nanoparticles are generated inside the swollen polymer network and not simply at its surface. It can be inferred that functional resins characterized by a narrower distribution of nanoporous domains will make it possible to control even more precisely the size and size distribution of the metal nanoclusters generated inside them, a task that we are going to turn to in the near future.

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.

An Alternative Explanation for the Negative Poisson's Ratios in Auxetic Foams

Auxetic materials exhibit the unusual property of becoming fatter when stretched and thinner when compressed, in other words they exhibit a negative Poisson’s ratio. A class of such materials which have attracted a lot of attention are auxetic foams which exhibit various enhanced physical characteristics. Foams with negative Poisson’s ratios (see Fig. 1) were first manufactured by Lakes and can be produced from commercially available conventional foams through a process involving volumetric compression, heating beyond the polymer’s softening temperature and then cooling whilst remaining under compression. Various two-dimensional models which represent a crosssection of foams have been proposed in an attempt to relate the experimentally measured values of the Poisson’s ratios to the microstructure of the foams. For example it has been proposed that conventional foams can be modelled using hexagonal and diamond-shaped honeycombs whilst the auxetic foams can be modelled through modified versions of these honeycombs. In the case of the 2D hexagonal honeycomb model, the required structural modification for auxetic behaviour requires the junctions connecting the honeycomb cell walls (‘ribs’) to be transformed during processing from ‘Y’-shaped joints to ‘arrow head’-shaped joints. For the diamond honeycomb model, auxetic behaviour requires selective removal in a regular manner of ribs during the transformation process. One should note that these two modifications need not be simultaneously applied for a foam or honeycomb to become auxetic. For example, the creation of acute angles in the hexagonal honeycombs through the conversion of the ‘Y’-shaped joints to ‘arrow head’-shaped joints is enough to make the honeycombs auxetic without the need of altering the topology of the cells by the removal of ribs. Although the above models probably play some role in modelling the auxetic behaviour in foams, and these models can reproduce the experimentally measured values of the Poisson’s ratios, one may argue that there is not enough experimental evidence to justify the assumption that either of these are the main structural modifications which result in the observed auxetic effect. For example, whilst there is experimental evidence that there are ‘broken ribs’ on the surface of the auxetic foams [see Fig. 1(b)], it is still not clear whether ‘broken ribs’ are also present in the bulk of the foam material. Also, the requirement in the diamond honeycomb model for the removal of ribs in a regular fashion is not likely to occur in the existing foam conversion process. In the case of the hexagonal models there is no clear experimental evidence that a majority of the ‘Y’ shaped joints in the conventional foam are converted to the required ‘arrow shaped’ joints during the compression/heat treatment process. In fact, one may argue that it is unlikely that the majority of the changes in the foam manufacture process are concentrated at the joints of the foam as one usually observes that the ribs of open cell foams are slightly thicker in the proximity of the joints than at the centre of the ribs. In view of this we propose a new model to explain the presence of negative Poisson’s ratios in foams. This new model is based on the hypothesis that it is more likely that changes in the microstructure during the compression/heat treatment process will conserve the geometry at the joints (i.e., they do not become re-entrant) and the topology of the system (i.e., there are no rib breakages, as was the case in the re-entrant systems) and instead, the major deformations will occur along the length of the ribs which buckle (the foam is typically subjected to ca. 30% compressive strain along each axis). Figure 1(b) provides clear evidence of the presence of buckled ribs in the transformed auxetic foam microstructure. We also assume that the additional thickness in the proximity of the joints will make it possible for the joints to behave, to a first approximation, as ‘rigid joints’. It is proposed that the rigid joints rotate relative to each other during the foam conversion process. The foam microstructure then ‘freezes’ in this much more compact form when the foam is cooled to below its softening temperature. An illustration of this is given in Fig. 2 which shows how a conventional two-dimensional hexagonal honeycomb in Fig. 2(a) (which can be treated as a two-dimensional model for conventional foams) can be converted through the compression/heat treatment process into an auxetic form shown in Fig. 2(b). We propose that the ‘rigid joints’ behave like ‘rigid triangles’ [Fig. 2(a)] which, during the heating/ compression process, rotate relative to each other to produce the more compact microstructure shown in Fig. 2(b). (This occurs though the formation of ‘kinks’ at the centre of the ribs which are the result of extensive buckling of the ribs in the compression/heat treatment process.) Uniaxial tensile loading of the idealised microstructure in Fig. 2(b) will cause a re-rotation of the triangles to generate the auxetic effect as illustrated in Fig. 2(c). (This corresponds to reFig. 1. SEM images of (a) conventional (non auxetic) open-cell polyurethane foams, and (b) auxetic open-cell polyurethane foam.

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.

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.