384 Chemistry & Industry 17 May 1999Materials can be divided into two basic categories: struc-tural or functional. Development of structural materialsis focused on improving their mechanical or physicalproperties, often with a saving in weight or cost. By contrast,functional materials are designed to detect and/or respond toevents or stimuli that occur during their lifetime. These materi-als often display novel and counterintuitive behaviour.Examples include electrically (semi)conducting polymers,materials that contract when heated, and those that expand whensubjected to hydrostatic pressure.Another example is a remarkable class of materials known asauxetic materials.1When stretched lengthways, these materialsget fatter rather than thinner (see Figure 1). As well as thisunique characteristic, auxetic materials have enhanced mechani-cal and physical properties, which means that they can actuallybe classified as both structural and functional materials.The key to auxetic behaviour is a value known as Poisson’sratio. This is defined as the ratio of the lateral contractile strainto the longitudinal tensile strain for a material undergoing uniax-ial tension in the longitudinal direction. In other words, it deter-mines how the thickness of the material changes when it isstretched lengthways. When an elastic band is stretched thematerial becomes thinner, giving it a positive Poisson’s ratio.Indeed, most solids have a Poisson’s ratio of around 0.2–0.4.Poisson’s ratio is determined by the internal structure of thematerial. For example, consider a two-dimensional honeycombdeforming by hinging of the ribs forming the network (seeFigure 1). For the conventional hexagonal geometry (see Figure1a), the cells get longer in the x-direction and close up along they-axis when the material is stretched along the x-axis, giving apositive value for Poisson’s ratio. Modifying the honeycombcell geometry to adopt a ‘bow-tie’ structure (see Figure 1b)means that the network gets longer in both the x- and y-direc-tions when it is stretched, giving it a negative Poisson’s ratio andmaking the material auxetic.2Auxetic materials are interesting both because of their novelbehaviour and because of enhancements in other material prop-erties that are related to Poisson’s ratio. For example, hardnesscan be increased in an auxetic material (see Figure 2). When anobject hits an auxetic material and compresses it in one direc-tion, the auxetic material also contracts laterally — material‘flows’ into the vicinity of the impact. This creates an area ofdenser material, which is resistant to indentation.Importantly, elasticity — and hence auxetic behaviour — doesnot depend on scale. Deformation can take place at the macro-,micro- or even molecular level (see Figure 3). This means thatwe can not only consider auxetic materials, but also auxeticstructures.Thinking bigOne of the largest examples of auxetic structures is the graphitecore found in some nuclear reactors. These cores were devel-oped in the late 1950s3and so pre-date the bulk of auxetic mate-rials research by some 30 years or so. Indeed, these structureswere not designed specifically to have auxetic properties.Instead, they were made to withstand the horizontal shear forcesgenerated during earthquakes, while also allowing free move-A triumph of lateral thoughtANDREW ALDERSON Imagine stretching elastic and seeing it get fatter rather than thinner. It may soundbizarre, but this property is what makes auxetic materials potentially so useful 1Auxetic behaviouryxyx(a) Non-auxetic materialAs the material is stretched the component cells get longer in the x-directionbut become compressed in the y-direction(b) Auxetic materialAs the material is stretched, the cells get larger in both the x- and y-directions2A harder materialAuxetic materials are more resistant to indentations than ordinary materials.An auxetic material contracts laterally when hit by an object — material effectively flows to the site of the impact rather than away from it. This makes the auxetic material more dense at the site of the impact and therefore moreresistant to indentationAuxetic materialNon-auxetic materialment of the structure in response to thermal movements betweenthe graphite core and steel supporting structures, and expansionand shrinkage of the graphite during exposure to radiation. Inother words, the structure had to have a high resistance to hori-zontal shear deformation and a low resistance to changes in vol-ume.A Magnox reactor core is made up of free-standing columnsof graphite bricks, with centralchannels for the fuel and con-trol rods. The bricks are con-nected by loose side and cornerkeys in keyways (see Figure 4).The structure expands in allradial directions when subjectto a tensile load and, further-more, retains its square latticegeometry during deformation.This makes the structure auxet-ic, with a Poisson’s ratio of –1in the horizontal plane. Forisotropic materials and struc-tures this value of Poisson’sratio corresponds to an infinite-ly high shear modulus withrespect to the bulk modulus —exactly the properties required in the design stage. The auxeticproperties were more a lucky result than a conscious part of thedesign, and it would be another two or three decades before thesignificance of this result would be fully appreciated and appliedto other materials and structures.Calling in the cellular foamsLarge-scale auxetic cellular structures were first realised in 1982in the form of two-dimensional silicone rubber or aluminiumhoneycombs deforming by flexure of the ribs.4These structuresare elastically anisotropic — that is, they have a differentPoisson’s ratio depending on the direction in which they arestretched. The current interestin auxetic materials really start-ed with the development in1987 of isotropic auxetic foamsby Roderic Lakes of theUniversity of Iowa (now at theUniversity of Wisconsin-Madison).5Polymeric andmetallic foams were made withPoisson’s ratios as low as –0.7and –0.8, respectively.6,7Whereas conventional foamsare made up of convex polyhe-dral cells, these new auxeticfoams feature much more con-voluted cell structures (seeFigure 5).8Foams have a variety of uses— in packaging, sound insula-tion, air filtration, shock absorption and as sponge materials, forexample. A range of properties have been studied for auxeticfoams. Lakes found that auxetic foams are more resilient