# Auxetic Materials - An Introduction

## Topics Covered

Background

How Do Auxetic Materials Work?

What Types Of Materials Can Exhibit Auxetic Behaviour?

Production of Auxetic Materials

Production of Auxetic Fibres

## Background

Pick up an elastic band and stretch it lengthways as if you were going to `ping' it at somebody. Before letting fly, look at the width of your elongated missile - it's thinner than an unstretched band, as you'd expect. Try this with an auxetic elastic band and you'd be in for a surprise. These bizarre materials can actually become fatter when stretched, a phenomenon which is now attracting the practical interest of many materials scientists.

Many people are sceptical about whether auxetic behaviour really exists, because we expect materials to behave like our elastic band and get thinner when stretched. Why is this? Do we base our expectation on a knowledge of the deformation mechanisms within the material? Or on classical elasticity theory? No, the only reason we think like this is down to everyday experience. Even the property relating directly to this behaviour, Poisson's ratio (ν), is defined so that most `normal' materials have a positive value.

## How do Auxetic Materials Work?

Poisson's ratio is the ratio of the contractile lateral strain to the tensile axial strain for a material stretched axially, and is typically around +0.2 to +0.4. However, when we look into classical elasticity theory we find that the Poisson's ratios of isotropic materials can not only take negative values, but can have a range of negative values twice that of positive ones.

A study of the structure of materials, and how it deforms, demonstrates that auxetic properties are entirely feasible. Figure 1 shows a 2D structure consisting of a regular array of rectangular nodules connected by fibrils. Deformation of the structure is by `hinging' of the fibrils. For the `open' geometry shown in figure 1a, the cells elongate along the direction of stretch and contract transversely in response to stretching the network, giving a positive v. However, modify the structure to adopt a `re-entrant' geometry, figure 1b, and the network now undergoes elongation both along and transverse to the direction of applied load. In other words, this is an auxetic structure.

Figure 1. Non-auxetic (a) and auxetic (b) deformation due to fibril hinging in a nodule-fibril microstructure.

## What Types Of Materials Can Exhibit Auxetic Behaviour?

But it is not just structures - some materials have an intrinsically negative ν. Auxetic behaviour is found in materials from the molecular level, up through the microscopic, and right up to genuinely macroscopic structures. Figure 2 shows that all the major classes of materials (polymers, composites, metals and ceramics) now exist in auxetic form and that natural and synthetic auxetic materials are known over several orders of magnitude of stiffness, or Young's modulus, E.

Figure 2. Auxetic materials form the molecular to the macroscopic level.

There is good reason to get excited about auxetic materials. As well as their novel behaviour under deformation, many other material properties can be enhanced as a result of having a negative Poisson's ratio. Typically such properties are inversely proportional to (1 - ν2) or (1 + ν), eg indentation resistance and shear modulus respectively. The negative limit of ν for isotropic materials is -1, and approaching this, the (1 - ν2) and (1 + ν) factors tend to zero, leading to enhancements in the related material property for auxetic over non-auxetic materials.

Enhanced indentation resistance has been demonstrated in auxetic foams. Auxetic carbon-fibre reinforced composites and microporous polymers have also shown similar benefits. The indentation resistance of auxetic ultra-high molecular-weight polyethylene (UHMWPE) is enhanced by up to a factor of three when compared with conventional UHMWPE. Other important properties known to be positively affected include shear resistance, fracture toughness, sound and vibration damping, and ultrasonic energy absorption.

## Production of Auxetic Materials

It is clear that auxetic materials have beneficial properties, so the next step is to produce them, and there are as many different routes as there are materials. Some routes rely on transforming non-auxetic materials into an auxetic form (foams), whereas others employ standard techniques but with novel material architecture to achieve the auxetic effect (honeycombs and fibre-reinforced composites). Still others require novel development of existing processing routes for conventional materials to produce auxetic functionality.

As an example of this latter scenario, take the processing of auxetic microporous polymers. The key is to produce a three-dimensional version in the polymer of the two-dimensional schematic in figure 1, i.e. to achieve nodules interconnected with fibrils. The route used to achieve this complex microstructure, for UHMWPE, is a batch process based on conventional polymer powder processing techniques of sintering and extrusion, but adapted so that there is only partial melting of the starting powder, which gives rise to fibrillation. An additional initial compaction stage can be used solely to impart some degree of structural integrity to the extrudates. This means the properties of the polymers can be tailored to fit the applications required and, by varying certain processing parameters, to produce everything from structural auxetic polymers with a Young's modulus of 0.2GNm-2, down to very auxetic, low modulus polymers.

## Production of Auxetic Fibres

Until recently only auxetic cylinders could be produced, which are difficult to use in real applications. However, at the ECCM9 conference in June 2000, the development of a continuous process for producing auxetic microporous polymer fibres was reported. Again, this has the distinct advantage of being based on a conventional processing route melt spinning, but with novel processing conditions required to achieve the nodule-fibril microstructure. Figure 3 shows the variation in width plotted against length variation for two polypropylene (PP) fibres stretched axially. Fibre 1 is a conventional PP fibre and shows a contraction in width as it is extended, corresponding to a positive ν. Fibre 2 is processed using extruder temperatures which lead to the nodule-fibril microstructure. Its width now increases upon stretching - it displays auxetic behaviour.

Figure 3. Width versus length variations for polypropylene fibres.

The ability to tailor the response of the fibre to give auxetic properties through processing is again evident. Polyproplylene filaments with diameters from 180pm to 1 mm, and Young's moduli in the range 0.2 to 2GNm-2 have been produced.

Primary authors: P.J. Stott, R. Mitchell, K. Alderson and A. Alderson

Source: Abstracted from Materials World, vol. 8, pp. 12-14, 2000