An auxetic material is one which has a negative Poisson’s
ratio, n1. This means that, unlike
an elastic band for example, which gets thinner when stretched,
an auxetic material will get fatter.
Equally, if an auxetic material is compressed, it will get
thinner. This interesting and counter-intuitive property is
found in some natural materials such as single-crystal arsenic2,
catskin3 and load-bearing cancellous bone from human shins4.
However, interest in this area really began to grow in 1987
when Roderic Lakes produced an auxetic polymeric foam at Iowa
University5. He achieved this by converting an ordinary foam
using a relatively simple process of heating and squashing6.
Since then, a whole range of synthetic auxetic materials have
been produced, including carbon fibre composites7, honeycomb
structures8 and microporous polymers9-11.
Auxetic materials are an unusual class of materials but,
apart from their novelty value, there are a number of reasons
why these materials are interesting. These all centre on the
possibility of enhancements in mechanical properties due to
a negative Poisson’s ratio as predicted by classical
elasticity theory. Take, for example, the case of the shear
modulus, G. This is given by:
(1) G = E/2(1+n)
So, as n approaches
–1, the shear modulus is predicted to become very large
indeed, provided that the Young’s modulus, E, is not
significantly affected. Similarly, in the Hertzian12 model
of elastic indentation resistance, the hardness, H, is related
to the Poisson’s ratio as:
(2) H µ (1-n2)-2/3
The hardness has been investigated for many of the synthetic
auxetic materials produced to date and enhancements have been
found across the board in materials as diverse as polymeric
and metallic foams13,14, carbon fibre composite laminates15
and microporous polymers16, where the auxetic form has been
found to be up to three times more difficult to indent than
conventionally processed polymers. Very recent investigations
into low velocity impact of auxetic carbon fibre laminates
have also shown enhancements in energy absorption of up to
a third for the first failure point17.
A further advantage of using auxetic materials which may
be of interest is their drapeability. Take, for example, a
panel structure, which may be typically in the form of a honeycomb
as illustrated in below. The problem with these materials
is that they cannot easily be curved into a doubly curved
or domed shape, rather the core forms a saddle shape on bending
(a). So, to produce
a doubly curved panel, it is necessary to either to machine
the required shape (thus wasting material) or to physically
force the panel to dome, resulting in considerable damage.
However, with an auxetic material, double curvature is readily
achieved (b).
So, auxetic materials are both novel and interesting due to
both their intrinsic behaviour and their properties.
REFERENCES
1. KE Evans, MA Nkansah, IJ Hutchinson and SC Rogers, ‘Molecular
network design’, Nature, 1991, 353, 124.
2. DJ Gunton and GA Saunders, ‘The young’s modulus
and Poisson’s ratio of arsenic, antimony and bismuth’,
J. Mat. Sci., 1972, 7, 1061-1068.
3. DR Veronda and RA Westmann, ‘Mechanical characterization
of skin – finite deformations’, J. Biomechanics,
1970, 3, 111-124.
4. JL Williams and JL Lewis, ‘Properties and an anisotropic
model of cancellous bone from the proximal tibial epiphysis’,
Trans. ASME, J. Biomech. Eng., 1982, 104, 50-56.
5. RS Lakes, ‘Foam structures with a negative Poisson’s
ratio’, Science, 1987, 235, 1038-1040.
6. RS Lakes, Polyhedron cell structure and method of making
same, Int. Patent Publ. No. WO88/00523, May 1987.
7. JP Donoghue and KE Evans, ‘Composite laminates with
enhanced indentation and fracture resistance due to negative
Poisson’s ratio’, 8th Int. Conf. Composite Materials
Honolulu, Hawaii, SAMPE, 1991.
8. IG Masters and KE Evans, ‘Models for the elastic
deformation of honeycombs’, Composite Structures, 1996,
35, 403-422.
9. BD Caddock and KE Evans, ‘Microporous materials with
negative Poisson’s ratios. I. Microstructure and mechanical
properties’, J. Phys. D: Appl. Phys., 1989, 22, 1877-1882.
10. KL Alderson and KE Evans, ‘The fabrication of microporous
polyethylene having a negative Poisson’s ratio’,
Polymer, 1992, 33, 4435-4438.
11. AP Pickles, KL Alderson and KE Evans, ‘The effects
of powder morphology on the processing of auxetic polypropylene’,
Polym. Eng. and Sci., 1996, 36(5) 636-642.
12. H Hertz, J. Maths. Crelle J, 1881 92.
13. N Chan and KE Evans, ‘Indentation resilience of
conventional and auxetic foams’, J. Cell. Plast., 1998,
34, 231-262.
14. RS Lakes and KJ Elms,‘Indentability of conventional
and negative Poisson’s ratio foams’, J. Comp.
Mat., 1993, 27, 1193-1202.
15. V Coenen, K Alderson, P Myler and K Holmes, ‘The
indentation response of auxetic composite laminates’,
6th Int. Conf. Deformation and Fracture of Composites, Manchester,
2001.
16. KL Alderson, AF Fitzgerald and KE Evans, ‘The strain
dependent indentation resilience of auxetic microporous polyethylene’,
J. Mat. Sci., 2000, 35 4039-4047.
17. V Coenen, K Alderson, P Myler and K Holmes, ‘The
low velocity impact response of auxetic composite laminates’,
to be presented at 8th Int. Conf. Composite Engineering, 2001.
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