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.

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.

Auxetic systems have the anomalous property of becoming wider when uniaxially stretched, i.e. exhibit a negative Poisson's ratio. One of the mechanisms which can give rise to this property is based on rotating rigid units, in particular 2D rigid polygons which are connected together at their corners through hinges and rotate relative to each other when uniaxially stretched. This work extends earlier preliminary work on connected rigid parallelograms and presents expressions for the mechanical properties for all the types of planar systems that can be constructed from rigid parallelograms of equal size connected at their vertices through flexible hinges. In particular, we derive and discuss the mechanical properties for the Type Iα, Iβ and IIβ rotating parallelograms which were not previously analysed and compare them with the properties of the Type IIα systems. We show that despite being rather similar to each other, the different types of ‘rotating parallelograms’ have very different mechanical properties and different abilities to exhibit auxetic behaviour.

Auxetic foams have been widely studied in view of their superior properties and many useful applications and various models have been developed to help explain the auxetic behavior in such foams. One such model involves the description of auxetic foams in terms of rotating units (e.g. the joints where different cell walls meet), a mechanism, which has also been observed experimentally. In the models, the rotating units are taken, to a first approximation, to be representable through rotating rigid triangles, which correspond to the 2D projection of these rotating units and although this model has been improved significantly since it was first proposed, current models still do not fully capture all the deformations that may occur in real foams. In this work, we propose an extended model which not only allows for relative rotation of the units (joints), represented by nonequilateral triangular units, but also for differing amount of material at the joints as well as deformation of the joints themselves, a scenario that is more representative of real auxetic foams. This model shows that, by permitting deformation mechanisms other than rotation of the triangles, the predicted extent of auxeticity decreases when compared to the equivalent idealized rotating rigid triangles model, thus resulting in more plausible predictions of the Poisson's ratios. Furthermore, it is shown that in the manufacturing process, a minimum compression factor, which is dependent on the amount of materials at the joints, is required to obtain an auxetic foam from a conventional foam, as one normally observed in experimental work on foams.

The effect of elevated temperature and solvent exposure on the microstructure of auxetic polyurethane foams is investigated. It is shown that such effects result in an expansion of the auxetic foams accompanied by the removal of the highly convoluted features in the microstructure of auxetic foams with the result that such foams lose their auxetic characteristics. It is also shown that such changes do not occur if the foams are subjected to the high temperature or solvent exposure in a contained state which does not permit the expansion. This means that auxetic foams can still be used in such environments provided that the right precautions are taken (e.g. putting them in a cover thereby constraining them to retain their volume).