Auxetics are materials that have a negative Poisson's ratio, meaning they become wider instead of narrower when stretched. The document discusses various auxetic materials including foams, honeycombs, composites, and nano-auxetics. Foams are one of the most common auxetic materials and their Poisson's ratio can be tuned through manufacturing processes like compression and annealing. Honeycombs made of materials like shape memory alloys can have auxetic properties and enhanced mechanical behavior. Composites incorporating auxetic components show improved properties over conventional materials.

1. Auxetics: From Foams to
Composites and Beyond
Fabrizio Scarpa,
f.scarpa@bristol.ac.uk
www.bris.ac.uk/composites

2. Contents
Introduction
Foams
Honeycombs and truss-cores
Composites
Nano-auxetics
Conclusions

3. Acknowledgements
Special thanks for their contribution to:
A. Bezazi, M. Bianchi, P. Pastorino, M. Ruzzene, C. Lira, C. D. L.
Remillat, L. G. Ciffo, M. R. Hassan, T. L. Lew, A. Spadoni, K.
Saito, C. W. Smith, W. H. Bullough, H. Abramovitch, M. Burgard,
M. Hoffmeister, M. Celuch, K. E. Evans, F. C. Smith, R. Neville,
C. Coconnier, S. Jacobs, J. Martin, M. Bruckner, A. Alderson, K.
Alderson, P. Innocenti, A. Lorato, Y. H. Tai,
J. Yates, K. Worden, A. B. Spencer and G. Tomlinson

4. Introduction
• From the Greek auxetos: “that can expand”
• Indicates Negative Poisson’s ratio (NPR) materials
 1    0.5 Homogeneous, isotropic solid
E1 21  E2 12 Special orthotropic solid


3 FR 2 1   2  Central deflection
of a clamped
16 Et 3 circular plate
1 Hardness – increase
H  with NPR – the
1    2 23
material wraps
around the indenter
Synclastic curvature – easy
manufacturing of dome-shaped
structures
(University of Bolton, 2008)

5. Introduction
Fibril Hinging
(microporous UHMWPE
and PFTE - GoreTex©)
A. Alderson, K. E. Evans, J. Mater. Sci. 1997, 32, 2797.
(courtesy of Azon.com)

6. Introduction
Rotating rectangles
J.N. Grima et al., Adv.
Mater., 12 (2000)1912;
A. Alderson et al.,
International Patent No.
(Courtesy of Professor Joseph Grima, http://home.um.edu.mt/auxetic/properties.htm) PCT/GB98/03281 (1998).
Used to prototype “smart” filters for chemical processes.
Possible explanation of auxetic behaviour in some forms of a-crystobalite

7. Introduction

y
r
t

x
(D. Prall and R. Lakes, Int. J.
Mech. Sci., 39, 305-314, 1996) LL
R
R
  30 o   L r   t r   b L
•Rotations of the nodes induce
bending of the ligaments
•Isotropic in-plane properties ( = -1)

8. Foams
Strain dependent tensile Poisson’s ratio
(Scarpa, et al. Phys. Stat. Solidi B, 242(3) 2005, 681-694 )

9. Foams
1. Multiaxial compression
4. Relaxation of Conventional 2. Annealing
the sample PU based foam
3. Cooling

10. Foams
Conventional PU foam
Auxetic ( = -0.26)
Non-auxetic iso-density

11. Foams
Compression is the most
significant manufacturing
parameter for
auxetic foams.
(M. Bianchi, F Scarpa, C W Smith. J. Mat. Sci. 43(17), 5851)

12. Foams
80
70
Conventional
r = 0.95 Iso density
60
]
Auxetic
3
50
Energy U [mj/cm
40
30
20
10
0
0 25000 50000 75000 100000
Number of cycles N

13. Smart auxetic foams
(F. Scarpa, W. A. Bullough and P.
Lumley, IMechE Proc. Part C, 216,
2004)
Doping auxetic foams with magnetorheological
fluids can provide a tuned acoustic absorber
with shift peak varying with the intensity of an
external magnet

14. Shape Memory effect
Auxetic Sample
Returned
Sample

15. Shape Memory effect
SEM images of
(a)conventional,
(Bianchi M., Scarpa F, Smith C. W., (b)1st auxetic,
2010. Acta Mater. 58(3), 858) (c)returned from (a) (b)
auxetic and
(d) 2nd auxetic
open-cell PU
based foam
(c) (d)

16. Foams – New manufacturing process
New manufacturing process
for Auxetic foams
(Bianchi M., Scarpa F. Banse M. Smith C. W., 2011. Acta
Mater. 59(2), 686)

17. Foams – Vibration transmissibility
9
8
Auxetic
7
Conventional
6
5
|X |
R
4
3
2
1
0
50 100 150 200
ω [Hz]

18. Centre-symmetric honeycombs
 4  2 

c 22 cos  cos   sin  2 sin Flexible topology to enhance
the mechanical and thermal
conductivity performance

19. Centre-symmetric honeycombs
Point A
INCONEL 617 core
Conduction – radiation problem
Time 0 s – uniform 273 K
Point B
Time 20 s – 1400 K at upper face
PPR configurations
NPR
configurations
In upper surfaces,
temperatures are lower for
auxetic configurations
(Innocenti P., Scarpa F, 2009. J. Comp. Mat. 43(21), 2419)

20. Centre-symmetric honeycombs
Shape memory alloy honeycombs

21. Centre-symmetric honeycombs
Nonlinear in-plane properties – SMA honeycombs
(Hassan MR, Scarpa F, Mohamed NA. Journal of Intelligent Material Systems and Structures 2009 20: 897-905 )

22. Zero  honeycombs (SILICOMB)
(Lira C, Scarpa F, Tai Y H, Yates J R,
2011. Comp. Sci. Tech. In press)
(Lira C, Scarpa F, M. Olszewska and M.
Celuch, 2009. Phys Status Solidi B 246,
2055)

23. Gradient honeycombs
(Lira C, Scarpa F., 2010. Comp. Sci. Tech. 70(6), 930)
(Lira C., Scarpa F. Rajasekaran R., 2011. J. Int. Mat.
Syst. Struct. In press)

24. Kirigami/Origami honeycombs
(Saito K,. Neville R. Scapa F., ICCS16
Porto, 28-30 June 2011)
(Saito K., Agnese F., Scarpa F, 2011.
J. Int. Mat. Syst. Struct. In press)

25. Chiral structures
•Developed using RTM techniques for maritime sandwich applications
•Core with polyester/glass fibre
•Superior specific compressive and shear strength compared to analogous cores
in marine constructions
•Possibility of embedding sensors (PZT, MFCs) for SHM or other monitoring
applications
•Flat or curved panels easily manufactured with no in-plane buckling stresses
•Developed and commercialised by CHISMATECH (Catania, I)
(Scarpa F., 2010. Comp.
Sci. Tech. 70.
CHISMACOMB Special
Issue)

26. Chiral structures
Truss-core beam
Applied torque
Deformed configurations for excitation at resonant frequencies:
Numerical
Localized deformations Localized deformations
1120 Hz 1150 Hz
Experimental
(Spadoni A,. Ruzzene M., Scarpa F, 2006. J. Int. Mat. Syst. Struct.
17(11), 941)

27. Chiral structures
Deflection vs Velocity at 15º
2.5
2
Experimental
Vertical Deflection (mm)
FEA Inviscid
1.5 FEA Viscous
1
Eppler420 for racecar wing design 0.5
0
(Bornengo D., Scarpa F., Remillat C D L., 2005.
0 10 20 30 40 50 60 70
Velocity (m/s)
IMechE Part G: J. Aerospace Eng. 219,185)
(Martin J. et al, 2008. Physica Status Solidi B Chiral wingbox provides continuous
245(3), 570) camber variation with a stiff bending
airfoil

28. ES
A
A
st
riu
m
U
LR
Ø
3m
SS
B
Fo R
ld
ab Ø
6m
le
Th Ti
in ps
Sh Ø
el 6m
lP
an
el
Ø
SM 6m
AR
T
A Ø
st 6m
ro
m
es
A h
st
ro Ø
9m
C m
hi es
ra h
lD Ø
ep 12
lo m
C ya
hi
ra bl
lD e
ep Ø
3m
C lo
hi ya
ra bl
lD e
ep Ø
6m
C lo
hi ya
ra bl
lD e
ep Ø
9m
Weight to Area Ratio
lo
ya
bl
e
Ø
12
m
Packed to Deployed Area Ratio
Deployable SMA antenna demonstrator

29. Auxetic composite laminates
(K Anderson, V R Simkins, V L Coenen, P J Davies, A Alderson, K Evans. Phys. Stat Solidi B, 242(3), 509 (2005) )
 = -0.156
 = 0.086
Static load/displacement curves Name0 Stacking sequence Name Stacking sequence Name Stacking sequence
ST 1 [± θ2 ]s ST 11 [± 33 /± θ ]s ST 21 [± 10 /± θ ]s
0.6
ST 2 [02 /± θ ]s ST 12 [± 35 /± θ ]s ST 22 [± 15 /± θ ]s
ST 8
0.3 ST 3 [902 /± θ ]s ST 13 [± 37 /± θ ]s ST 23 [±16 /± θ ]s
ST 10
ST 12
ST 4 [- θ/+ θ/- θ/+θ/]s ST 14 [± 40 /± θ ]s ST 24 [± 17 /± θ ]s
0 ST 14
0 20 40 60 80 100 ST 5 [± θ/ 02]s ST 15 [± 45 /± θ ]s ST 25 [± 18 /± θ ]s
 13
ST 15
ST 16
-0.3 ST 6 [± θ/902 ]s ST 16 [± 50 /± θ ]s ST 26 [± 19 /± θ ]s
ST 17
ST 18 ST 7 [± 20 /± θ ]s ST 17 [± 60 /± θ ]s ST 27 [± 21 /± θ ]s
-0.6 ST 19
Carbon ST 3 ST 8 [± 25 /± θ ]s ST 18 [± 70 /± θ ]s ST 28 [± 22 /± θ ]s
-0.9 ST 9 [± 27 /± θ ]s ST 19 [± 80 /± θ ]s ST 29 [± 23 /± θ ]s
 [Degrees]
ST 10 [± 30 /± θ ]s ST 20 [± 5 /± θ ]s ST 30 [±24 /± θ ]s
(E H Harkati, A Bezazi, F Scarpa, K Alderson, A Alderson. Phys. Stat Solidi B, 244(3), 883 (2007) )

30. Auxetic composite laminates
3-point bending (T300-914 prepreg)
(Bezazi A., Boukharouba W., Scarpa F, 2009. Physica Status Solid B 246(9), 2102)

31. Auxetic composite laminates
3-point bending (T300-914 prepreg)
(Bezazi A., Boukharouba W., Scarpa F, 2009. Physica Status Solid B 246(9), 2102)

32. Nano-auxetics in carbon structures
Weakening of C-C bonds strength → NPR in SWCNTs
(Jindal P., Jindal VK, 2006. J. Comp. Theor. Nanosci. 3(1), 148)
NPR effect when bond angle variation dominant
deformation mechanism modification of force
constants and bond length equilibrium
(Yao, YT, Alderson A, Alderson K., 2007. Paper presented at Auxetics 2007
@ Malta)
Evidence of in-plane NPR in
buckypapers when mixing Other possible
SWCNTs and MWCNTs mechanisms?
(Hall, LJ et al, 2008. Science, 320, 504)

33. Nano-auxetics in carbon structures
Missing rib model (MRM) to explain
NPR in open cell foams
(C. W. Smith, J. N. Grima and K E Evans, 2000. Acta Mater. 48, 4349)
Vacancy defects induced by electronic or ion irradiation
(Telling, R. H. et al, 2003. Nature Mat. 2, 333)
(Ajayan, PM, Ravikumar, V, Charlier, JC, 1998. Phys. Rev. Lett. 81, 1437)
(Mielke, SL, et al, 2004. Chem. Phys. Lett. 390, 413)
Uniaxial mechanical
properties depending on %
of vacant atoms
(Sammalkorpi M et al. 2004. Phys. Rev. B 70, 245416)

34. CNT and graphene mechanical properties
(F Scarpa and S Adhikari, 2008. J. Phys. D: App. Phys., 41, 085306)
(Scarpa F., Adhikari S., Phani A S, 2009. Nanotechnology 20 065709)
(Scarpa, FL, L. Boldrin, Peng, H-X, Remillat, CDL & Adhikari, S., 2010. Applied Physics Letters, 97,
151903)
(R. Chowdhury, Adhikari, S, CY Wang & Scarpa, FL., 2010 Comp. Mat. Sci., 48, 730)
(E.I. Saavedra Flores, Adhikari, S, Friswell, MI & Scarpa, FL, 2011. Comp.Mat. Sci., 50, 1083)
(Scarpa, FL, J. W. Narojczyk & K. W. Wojciechowski., 2011., Physica Status Solidi B, 1, 82
(Chowdhury R, Adhikari S, Rees P., Wilks S. P., Scarpa F., 2010. Phys. Rev. B 83, 045401)

35. Nano-auxetics in carbon structures
•FE nonlinear tensile loading
simulations – applied strain 1.e-3
•Random generation for vacancies
•Elements attached to vacant
atoms desactivated (ekill utility)
•Combinations of SWCNT aspect
ratio, radius and % of vacant
atoms considered
•12800 MC simulations
(F Scarpa, S Adhikari, C Y Wang 2009. J. Phys. D: App. Phys., 42(14), 142002)

36. Nano-auxetics in carbon structures
Mean Young’s modulus ratio and standard deviation Young’s modulus ratio for
armchair (n,n). ● = 2 % NRV; ■ = 1.5 % NRV; ▲= 1 % NRV; ◊ = 0.5 % NRV
(F Scarpa, S Adhikari, C Y Wang 2009. J. Phys. D: App. Phys., 42(14), 142002)

37. Nano-auxetics in carbon structures
Probability density functions for nrz in Distribution of the standard deviations
(n,n) tubes (R = 0.426 nm, AR=5) for (n,n) configurations (pristine nrz
between 0.29 and 0.16)
(F Scarpa, S Adhikari, C Y Wang 2009. J. Phys. D: App. Phys., 42(14), 142002)

38. Nano-auxetics in carbon structures
(F Scarpa, S Adhikari, C Y Wang 2009. J. Phys. D: App. Phys., 42(14), 142002)
(6,0) rz = -0.41
Evidence on NPR in defective CNTs found in NI-CNT systems
(Smolyanitsky A, Twari V K, 2011. Nanotechnology 22 085703)

39. Nano-auxetics in carbon structures
(Ma Y et al, 2010. App. Phys. Lett. 97 061909)

40. Nano-auxetics in carbon structures
(Chen L et al, 2009. App. Phys. Lett. 94 253111)

41. Conclusions
Auxetics and NPR can be engineered at different scales
Use of auxetic materials and structures needs lateral
thinking  multidisciplinary research
There is scope for R&D activities at different TRLs –
from blue sky to manufacturing of commercial
prototypes

42. Conclusions
Thank you for
your attention!