Thought Leaders

An Introduction to Auxetic Materials

Professor Andrew Alderson, Principle Research Fellow at the Materials and Engineering Research Institute (MERI) at Sheffield Hallam University, talks to AZoM about his work with Auxetic Materials, including applications and the future of their development.

Could you please give a brief description of what an Auxetic material is?

An auxetic material becomes thicker in one or more width-wise directions when it is stretched along its length. Conversely, it becomes thinner when compressed lengthwise. This contrasts with ‘normal’ materials which tend to thin when stretched – think of stretching an elastic band, for example – or thicken when compressed. The defining property of an auxetic material is, then, that it possesses one or more negative Poisson’s ratios (as opposed to the positive Poisson’s ratio displayed by ‘normal’ materials).

Do you have any specific examples of auxetic materials?

The range of materials includes natural and man-made. It covers from large-scale structures right down to the nanoscale, and it spans the classic categories of polymers, composites, metals and ceramics. So in terms of natural materials, we can look at naturally-occurring crystalline silicates; α-cristobalite is known to be auxetic.

There are also related materials such as zeolites and a number of those are known now to be auxetic. On the bio-materials side, a number of skin tissues and soft tissues have reported to be auxetic, and there are hints that some forms of bone are auxetic. In addition, early stage embryonic tissue has been reported to be auxetic. It looks as though in nature we're starting to scratch the surface and discover more materials that are auxetic.

In terms of man-made ones, let's start at the macro scale. I would say the largest man-made auxetic structure I am aware of was probably designed in the 1950s in the case of the graphite core in a number of nuclear reactors. So, on the scale of graphite blocks that are of metres dimensions, you can get structures that are auxetic.

Auxetic foam

Auxetic foam. Image Courtesy: MERI

Moving down a little bit from the extreme macro scale, we'll see things like honeycombs, and other cellular truss-like structures, can be auxetic. Then we get into things like foams. We're aware of metallic, ceramic and polymeric foams that are auxetic. Going down further, we can make microporous polymers, or microcellular foams, in auxetic form.

You get into things like carbon-fibre reinforced epoxy composite laminates. The way you arrange the layers (or plies) in those composites you can end up designing in the auxetic effect and making rigid auxetic composites. We're getting into things like microfabricated versions of some of those I just mentioned, so scaling down two dimensional and three dimensional cellular structures using 3D printing processes, LIGA techniques, and other microfabrication techniques. We're getting into interesting materials with features of the size of a few microns.

Going down even further, you then get into the molecular or nanoscale structures. So I mentioned, for example, earlier in the naturally-occurring silicates, α-cristobalite and α-quartz in certain directions and under certain temperatures can be auxetic. We're also aware of things like natural crystalline polymers, so certain forms of crystalline cellulose are known to be auxetic.

What effect does having a negative Poisson’s ratio have on the properties of these materials? Are there any adverse effects on some properties?

Look through any good standard textbook on materials elasticity, or do an internet search, and it won’t take you long to identify a number of expressions relating other material properties to the Poisson’s ratio of the material. Historically, when looking to optimise or achieve extreme values of such properties, the Poisson’s ratio of the material was generally assumed to have a value that could not be changed, typically having a positive value of around +0.25 to +0.33 for most materials.

The development and discovery in recent years of materials that can have a negative value of Poisson’s ratio, and our ability to tailor it’s magnitude through manufacturing to modify the underlying internal material structures and deformation mechanisms, have led us to reconsider the role of Poisson’s ratio in the development of materials having enhanced properties. We now realise that a negative Poisson’s ratio can lead to very dramatic enhancements in other properties not easily achieved with positive Poisson’s ratio materials.

For example, if we consider isotropic linear elastic materials then the elastic response of the material is described fully by just 4 inter-related properties: Poisson’s ratio, Young’s modulus, shear modulus and bulk modulus. The range of Poisson’s ratio for isotropic materials is restricted to between -1 and +0.5.

From the relationship between shear modulus, bulk modulus and Poisson’s ratio it turns out that the positive limit for Poisson’s ratio (corresponding to rubber) provides a material that is easy to deform (through shearing) but is relatively incompressible. On the other hand, the negative limit for Poisson’s ratio of -1 produces a material that is difficult to shear (i.e. it maintains shape) but is relatively compressible (changes volume easily).

Similar considerations, and experimental testing, have shown auxetics can lead to a range of other property enhancements, including for example:

  • enhanced indentation resistance (arising from a tendency of the material under the indenting object to densify both along and transverse to the indentation direction for an auxetic material)
  • enhanced fracture toughness
  • a natural tendency to produce dome-like curvature in plate-like material under pure bending, as opposed to the saddle-shape adopted by a positive Poisson’s ratio material
  • enhanced porosity variation when stretched or compressed
  • enhanced energy absorption (impact, vibration, ultrasonic)
  • enhanced ‘anchorability’ through ease of insertion into a surrounding material due to lateral contraction in response to the compressive insertion force; and resistance to removal through ‘locking in’ due to lateral expansion when placed under a tensile removal force

When we consider anisotropic auxetic materials the range of values that Poisson’s ratio can take in any given direction becomes infinite. This can produce additional enhancements. For example, a material with a directional Poisson’s ratio of -10 will undergo an order of magnitude more strain in the transverse direction than in the loading direction, leading to strain amplification.

Enhancements are also to be found when combining auxetic materials with other materials to form composite systems. The aforementioned ability to resist extraction from a surrounding material when placed under tension means that a composite containing auxetic fibres has enhanced fibre pull-out resistance.

A piezoceramic composite containing piezoelectric ceramic rods in an auxetic polymer matrix should have enhanced electromechanical coupling. The thermal expansion behaviour of carbon fibre reinforced epoxy composites can be tuned by introducing auxetic inclusions, with significant potential to reduce microcracking and distortion normally associated with residual thermal stresses in such systems.

In terms of any adverse effects, it really depends on the property you are after. So, returning to the first example, if you want a material that can change shape very easily but is relatively incompressible then auxetic materials may not be the way forward. The key is to understand the relationship between Poisson’s ratio and the property (or combination of properties) required for specific applications.

Is the auxetic property typically anisotropic in nature, so for example in a rectangle would you only observe the phenomenon for stretching in the transverse direction and not necessarily when stretching in the longitudinal direction?

Usually, for most materials and systems, we have to comply with what we call the “symmetric compliance matrix”. So, in the example you just mentioned, if you have a rectangular, 2D auxetic material and you pull it in the horizontal direction, it would almost certainly be auxetic in the other direction, when you pull it in the vertical. It might be slight in one and very large in the other, but providing the material complies with classical elasticity theory - which many materials do, of course - then that should be the case.

Left: Auxetic foam relaxed. Right: Auxetic foam in tension.

Left: Auxetic foam relaxed. Right: Auxetic foam in tension. Image Courtesy: MERI

Where you might get a difference in the same plane is not pulling either horizontally or vertically, but if you pull in an off-axis direction, so for example 30 degrees to the horizontal, you may well then get a different, positive Poisson's ratio. Within a plane, you can get different signs [positive or negative] of Poisson's ratio, but for each pair of mutually orthogonal directions you should ordinarily have the same sign.

Now, when you get to three-dimensional material, though, for instance a cuboid, you can imagine the situation where you're pulling in the axial direction and in one of the lateral directions it's auxetic, but in another lateral direction, even though it's pulled in the same direction, it's conventional. We certainly do that in my group for the polymeric foams, for example. We can process foams that have different values of Poisson's ratio in different planes.

What are the potential applications for these materials? What industries in particular could benefit from their use?

Well, the auxetic effect is already being exploited in some products and applications, albeit unintentionally or unknowingly in some cases. Perhaps the most obvious example is the expanding Hoberman sphere educational toy beloved by USA presidents and children the world over, and which is inspiring real-world applications in deployable and domed structures for shelters and buildings.

Going back in time, many graphite core structures of nuclear reactors developed in the 1950s were designed to retain their shape (in the event of an earthquake) but allow for expansion or contraction (due to thermal and radiation effects). This is precisely the combination of shear resistance and compressibility we now expect for an auxetic material and, as already noted, the graphite structures are, indeed, auxetic in the transverse plane.

Over very large timescales, and thinking of materials rather than the structures referred to just now, we are discovering that nature has evolved a number of biomaterials with the auxetic effect. We are trying to understand now why nature has done this, but it is likely to be relevant to the application for which the material has been developed.

Bovine common carotid arteries display auxetic character, for example. Could it be that the auxetic character leads to a reduced tendency for blood vessel rupture due to the enhanced fracture toughness of auxetics? Or perhaps it is related to the control of blood flow through the artery.

A simple consideration of a blood vessel made from isotropic elastic material shows that the inner lumen of the artery or vein retains the same cross-sectional area under variations in blood pressure if the material has a Poisson’s ratio approaching the auxetic limit of -1, which has implications on blood flow. Understanding why and how nature has developed auxetic materials is providing impetus for the development of new and improved man-made materials.

Turning to products being developed more recently, we are seeing an increase in the number of patent applications being filed for auxetic products, and these are now being successfully brought to market. Here an example is the Under Armour Micro G Drive “Volt” sports shoe which contains an auxetic shoe upper.

The auxetic benefits include improved comfort and fit of the sports shoe to the complex size and shape of the foot at rest and during sporting activity. At Sheffield Hallam University we see sporting applications as an area of future growth for auxetics and I am working with sports engineers in our Centre for Sports Engineering Research to develop impact protection systems which exploit dramatically enhanced impact properties of auxetic components (mimicking the natural auxetic armour protection system developed by nature in some sea-shells).

Most applications development work to date has probably been related to the aerospace and other transport sectors. Here applications include vibration damping structures and materials, curved components (e.g. nose cones), morphing (shape change) structures, composites having reduced damage (and replacement) potential, cleanable filters, and lighter composite components.

Healthcare and biomedical devices represent another area where auxetics are increasingly being seen as offering solutions in delivering technologies for more effective treatment. These include arterial prostheses, artificial spinal disc implants, dilators and stents, space creation and organ retraction devices for laparoscopic surgery, drug-delivery systems, ultrasonic imagers, ophthalmic devices, hip implant devices, scaffolds for tissue engineering, and annuloplasty prostheses.

Other sectors where auxetic applications are under development include defence (e.g. blast curtains and impact protection components) and apparel (garments having increased comfort and fit).

With naturally-occurring auxetic materials, do you need to have a lot of manipulation of them before they can be used in practical applications?

The chances are that they've evolved over many years by nature of the current applications that they are used in, so they’re probably already in a practical application that they are optimised for. In terms of biomaterials, you use them in a natural state. If you're going to do a graft of a soft tissue, then it's there, you do no more than what you currently have to do to move one piece of skin to another location.

If we look at the example of cristobalite, the auxetic behaviour has been measured in single crystalline form, and it's anisotropic so you get different values and signs of Poisson’s ratio in different directions. Interestingly for α-cristobalite, when you do the averaging to come up with a polycrystalline aggregate Poisson’s ratio, you end up with an overall isotropic auxetic material.

So if you wanted an auxetic filler, for example, to put into a composite system in some way to benefit from the auxetic property, then polycrystalline α-cristobalite powder is an interesting material that you may be able to use with minimal further processing before you can use it.

You mentioned healthcare and biomedical devices that could use auxetic materials. There are a lot of existing dominant materials in this market such as titanium alloys, ultra-high-molecular-weight polyethylene (UHMWPE), and ceramics, typically alumina, so in what way do you think auxetic materials could offer benefits over these?

Well, we might not offer benefits over them, but we might make variants of them that are auxetic. For example, if you think about a hip implant made out of titanium alloy, there are certain reasons for doing that, but one of the problems is that titanium alloy is much stiffer than the bone into which the implant is inserted.

Now, that can create problems in terms of things like stress-shielding, and what that means is the body weight is essentially carried by the titanium alloy, and that gives you problems at the distal end of the implant. You get growths of bone which can be very painful, because it's overloaded due to the stress going down the implant stem.

At the top end of the stem, the bone is relatively unloaded where the stem is, so that becomes quite weak and can fracture and fail. So you get painful bone growth at the bottom of the implant and weak fracture-prone, material at the top end of the implant.

The way to get around that is to think about making implants that are not as solid as titanium alloy, for example a titanium mesh. Some of the work that we've done recently says that if you can make that mesh in an auxetic form, then not only can you get a better match of the [Young’s] modulus of the mesh with the bone into which you're implanting it, but you also improve the stress shielding effect.

You also get other benefits, such as it can be easier to insert into the bone cavity to start with, or you require a slightly smaller bone cavity to prepare before you put the implant in. Both of those will help with the healing process because you've removed less bone in the first place.

Over time where the implant is loosened - and therefore at the moment you require revision replacement operation - we can design auxetic implants where you can put in a tightening mechanism. So you'd require a rather less aggressive operation that would then enable you to re-tighten the implant and preserve and, in fact, enhance the lifetime of the device.

With UHMWPE when you think about the hip implant and when you think about the socket of the implant, UHMWPE is the gold standard for those sorts of socket linings, for very good reasons, such as wear resistance. We believe that if we use an auxetic version of UHMWPE, and auxetic UHMWPE can be made, then we believe that the auxetic effect will ultimately give us improved wear resistance.

So, again, it won't be replacing the material, we'd just be making it in an auxetic form to give it optimised properties for the application which it's currently being used for.

As with a lot of fantastic innovations, there is difficulty when scaling up production to a manufacturing scale. Do you believe this will be an issue for auxetic materials too?

It all depends on the particular type of auxetic material you are considering. In some cases the use of auxetic materials will improve the manufacturing of the product. In the recent sports shoe, the auxetic material naturally conforms to the multiple curved surfaces required in the formation of the shoe upper. This means that the shoe upper can be produced using fewer pieces of material (in fact it can be formed from a single piece), thus reducing the need for cutting and sewing processes that are required for conventional material shoe uppers.

The use of auxetic inclusions to tailor the thermal response of carbon-fibre reinforced composite laminates is another example where manufacturing will be greatly improved. Ultimately, it will remove, or significantly reduce, the current need for additional so-called ‘balancing’ layers in the composite. This will not only reduce the amount and cost of expensive carbon fibre, but will also greatly simplify the complex design processes required for current composite laminate components.

Some auxetic materials use exactly the same starting materials and manufacturing processes as conventional materials. Examples here include auxetic carbon-fibre composite laminates (as opposed to laminates containing auxetic inclusions) and auxetic knit fabrics. So in these cases, there are no differences in production throughput or cost.

Other examples use existing manufacturing processes and starting materials, but with processing parameters that are unusual or require careful control, placing restrictions on production volume and/or cost. The production of auxetic polymeric monofilaments and films using melt extrusion is a case in point.

These are usually processed at a temperature in the vicinity of the melting temperature of the starting powder, requiring relatively slow throughput speeds. The process has been successfully scaled up to commercial scale extruders, but production volume currently remains significantly lower than commodity conventional monofilaments and films.

Equally, the production of auxetic ‘double helix’ yarns, comprising wrap and core components, and auxetic fabrics made from them, require very careful positioning and/or fixation of the wrap component, and close control over alignment of adjacent yarns, respectively, thus complicating the manufacturing processes compared to conventional wrap yarns and fabrics.

So there is scope for further research and development to move these types of auxetic materials towards wider commercial production, and this is something we are actively pursuing at Sheffield Hallam in the case of extruded fibres and films.

Then there are auxetic materials for which manufacturing processes for existing conventional equivalents cannot be used. This can be a significant barrier since it means an alternative process is required, along with the associated costs in setting up processing plant. To a degree this has been the case for auxetic honeycombs.

The commercial ‘glue and pull’ process used to produce conventional hexagonal aluminium honeycombs, for example, cannot be used to make the auxetic ‘re-entrant’ hexagonal equivalent. However, recent developments in rapid prototyping and other techniques such as kirigami, as well as the development of alternative honeycomb geometries, are overcoming this barrier to commercial production.

Finally, there are those auxetic materials that require conversion of a conventional material into the auxetic form. This has additional time and cost penalties since it requires a post-processing stage compared to the conventional material itself. The first reported synthetic auxetic material, auxetic open-cell foam, is a case in point here: a conventional foam is effectively subject to compression and heat treatment to produce the auxetic foam.

Variants on this process include replacing the heating stage with a solvent stage, but as yet a process to make an auxetic foam direct from the foaming process has not been reported.

How do you see auxetic materials developing in the future? In particular, how do you believe the research being conducted at Sheffield Hallam University will be involved in this development?

I think the future developments of auxetics will look at things like incorporating the auxetic effect with some other functionality effect. So you might want to make conductive auxetics for future applications. So multi-functionality, I think, is key. I think the ability to scale down to the nanoscale and effectively design intrinsic auxetic behaviour into materials is another key area.

The ability to make auxetic materials with gradient structure and properties is another area I see significant potential for – ensuring the material has the right function/property at the right place for the application. We’ve done quite a bit of work on gradient auxetics recently.

Expanding the range of auxetic materials that are available and, in so doing, increasing the awareness within industry of the auxetic effect and its possibilities is going to be critical in accelerating commercial uptake. I think tying in with things like advances in manufacturing to help us expand the range of auxetics will be important, and equally auxetics will be involved in improving manufacture processes.

Where do I think the work at Sheffield Hallam is going to fit in with that vision? I think one of the key areas at the moment is learning from nature. I'm a firm believer that nature has evolved materials over the years to optimise function for the application. So we're trying to understand how nature makes materials auxetic, why it's done that, and where we can then apply that in new materials and potential applications.

The sorts of sectors that we're looking at, we've done quite a bit of work in the past that's been relevant to aerospace and transport. More recently, my group is now looking at healthcare. We're working, for example, with a team of surgeons to develop an expandable device for laparoscopic surgery based on auxetic principles. I think healthcare is the next sector to follow on from aerospace in terms of auxetics, and is one that we're addressing.

I think the other part that I'm conscious of is that both healthcare and aerospace have quite long qualification periods and, therefore, lead times. It's important for the field to get more applications out there than are currently there and to do that quite quickly. So I'm looking at less-regulated sectors.

For example, I'm working with sports engineers here [at Sheffield Hallam] to develop auxetic materials for next-generation sporting technology. I'm working with architects and looking at schemes for buildings and shelters, and that nicely comes back to natural materials, where I started at. We've actually very recently just developed a structured architectural skin concept, based on the arrangement of collagen fibres in natural auxetic skin.

Those are the sorts of current areas that we are prioritising here at Sheffield Hallam. It's looking to expand commercially and doing that in some areas where there are some very clear applications, but also trying to accelerate that by looking at less-regulated sectors.

About Prof. Andrew AldersonAndrew Alderson

Prior to joining the Materials and Engineering Research Institute at Sheffield Hallam University in 2013, Andrew was Director of the Institute for Materials Research and Innovation, Head of Sciences and Professor of Materials Physics at the University of Bolton.

He has also worked in the Nuclear industry (BNFL), held Directorships with two companies, and played leading roles with industry-facing collaborative research centres, consortia and networks.

He has served on 6 EPSRC panels (including panel chair), published around 130 papers, and is co-inventor on 14 patent applications.

He has appeared on BBC TV and Radio, and had his work exhibited in the Science Museum (London). Awards include the Kenneth Harris James prize of the Aerospace Industries Divisional Board of the IMechE.

Andrew's main research focus is on advanced and smart materials having unusual mechanical and thermal properties for applications in the transport, healthcare technologies, advanced manufacturing and low carbon sectors. A major activity is research into auxetic (negative Poisson's ratio) materials, including auxetic polymers, composites and inorganics from the nanoscale to the macroscale.

Disclaimer: The views expressed here are those of the interviewee and do not necessarily represent the views of Limited (T/A) AZoNetwork, the owner and operator of this website. This disclaimer forms part of the Terms and Conditions of use of this website.

Alessandro Pirolini

Written by

Alessandro Pirolini

Alessandro has a BEng (hons) in Material Science and Technology, specialising in Magnetic Materials, from the University of Birmingham. After graduating, he completed a brief spell working for an aerosol manufacturer and then pursued his love for skiing by becoming a Ski Rep in the Italian Dolomites for 5 months. Upon his return to the UK, Alessandro decided to use his knowledge of Material Science to secure a position within the Editorial Team at AZoNetwork. When not at work, Alessandro is often at Chill Factore, out on his road bike or watching Juventus win consecutive Italian league titles.


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  1. gowreeswari bheesetti gowreeswari bheesetti India says:

    which properties may vary in auxetic materials comparing to individual elements?

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