Journal Club April 2010: Negative Poisson's ratio materials

Ajay Bangalore Harish

Firstly, I apologize for the previous comment. I had some problems posting using Chrome & it did not allow me to delete it. I was reading some of the papers that have been linked in the article. It seems a pretty interesting line of research. I had two questions:

1.One of the ways this behavior is explained is by a hinge phenomenon. So as an extensional load is applied, this results in the hinge to open & causes a positive strain in the transverse direction. In that sense there would need to be a theoretical limit to this behavior (i.e. the negative poisson ratio)? If so, wouldn't it be more like two regimes (one where the poisson ratio is negative & then further over a certain load where it might go to a positive poisson ratio regime) or its like a fixed material property?

2.  Also how would these materials behave in the case of a cyclic loading (i.e. something like failure by fatigue)?

Thanks

Ajay

This subject is indeed very interesting.

I find that most papers concern the design of materials with negative Poisson ratio. Thus there are so many types of NPR materials. Are there any more general and more theoretical researches on these materials?

A good intro, Katia, but you miss an important reference.  This web site .  A few lines from the site which has animations, etc. etc.

Negative Poisson's
ratio materials

[Rod Lakes,
University of Wisconsin]

Search tool

Michele Ciavarella, http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
blogs http://rettorevirtuoso.blogspot.com/
YouTube Channel http://www.youtube.com/user/RettoreVirtuoso

Katia, for my MilleChili journal and project, I mean for a top performance car, or let's say even for a F1 car, with very large budgets, are these objects any realistic in the near future?

If not what are the limitations to real production?  Thanks for answer. Mike

Choi, J. B. and Lakes, R. S., "Design of a fastener
based on negative Poisson's ratio foam", Cellular Polymers, 10,
205-212 (1991).
In this article we make use of the negative Poisson's ratio of recently
developed cellular solids or spongy materials in the design of a
press-fit fastener. Insertion
of the fastener is facilitated by the lateral contraction which negative
Poisson's ratio materials exhibit under compression. Removal of the
fastener
is resisted by the corresponding elastic expansion under tension.
Get pdf

Lakes, R. S., "Design considerations for negative Poisson's ratio
materials" ASME Journal of Mechanical Design, 115,
696-700, (1993).

This article presents a study of the implications of negative Poisson's
ratios in the design of load bearing structural elements. Stress
concentration factors are reduced in some situations, and unchanged or
increased in others, when the Poisson's ratio becomes negative. Stress
decay according to Saint Venant's principle can occur more or less
rapidly as the Poisson's ratio decreases. Several design examples are
presented, including a core for a curved sandwich panel and a flexible
impact buffer.
Get pdf
Curvature of negative Poisson's ratio honeycomb during bending is convex
in contrast to the saddle shape usually seen for positive Poisson's
ratio, and is shown in the animation at the right and in this video

Michele Ciavarella, http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
blogs http://rettorevirtuoso.blogspot.com/
YouTube Channel http://www.youtube.com/user/RettoreVirtuoso

I wonder if there's been any work in analyzing defects in  metamaterials. If one link breaks, how much do the properties change? Does it have to do with the connectedness of the force-network? If one link breaks, does the instability spread? Furthermore, can one think of imperfections analogous to edge dislocations and write down closed form expressions for resulting stresses as in  http://en.wikipedia.org/wiki/Dislocation

-Nachiket

Carl T. Herakovich, University of Virginia

You may be interested to know that negative Poisson's ratios were observed in laminated composites as early as 1984 ( J. Composite Marerials, Vol. 18, pp. 447-455, 1984). 

I guess it must be a difficult one, but you should be challenged then, instead of giving up already!

I mean is all this fuss about negative Poisson's a mathematical excercise, with curiosity, or is it a real breakthrough which can open new avenues in research, say in cancer, in malaria, in new materials like when the (last) Italian Nobel Prize winner Prof. Giulio Natta invented plastics?

Being at Harvard as a brigth and brilliant italian young promise, I am sure you should be aiming at Nobel prize type of research, not just avenues of research already exhausted.  This seems to me quite old stuff, has been postulated to work already 30 years ago if not earlier, companies are already there to try to something (but I suspect the turnover is minimal), so why should we waste more time with it?

Sorry to be direct, I guess you understand what I mean.

If not Natta, lookat Subra Suresh's research across the street from Harvard, and you'll find possibly Nobel prize research.  Or, stay at MIT, and look at the other italian brigth guy Francesco Stellacci.  Maybe he has elasticity problems which are really worth solving, worth ask him!

Francesco Stellacci begin_of_the_skype_highlighting     end_of_the_skype_highlighting

Paul M. Cook Career Development Associate Professor
of Materials Science and
Engineering

Doctorate, Materials
Science and Engineering, Politecnico
di Milano, 1998

Room 13-4053,
77 Mass. Ave., Cambridge, MA  02139
617-452-3704
(phone)
frstella@mit.edu

Professor
Stellacci's research group

Professor Stellacci's research interests are in
nano-science and nano-technology, specifically in the investigation of
the structure-property relationships that exist between nanostructured
molecular assemblies and their surface properties.

His research focuses on the
generation of new understanding on the assembly of molecules in
spatially defined arrangements and their interactions with organic and
bio molecules and with inorganic surfaces. The goal is to apply this
knowledge toward the development and the efficient fabrication of
original nano-size molecular-based materials and devices for a wealth of
applications. In order to build such devices, Stellacci’s group is
developing new materials (organic ligand coated nanoparticles and
nanotubes), and new soft-materials fabrication techniques (based on
molecular recognition and self-assembly). A specific example is the
discovery of novel materials whose outside shell spontaneously assembles
in ways that resemble the structuring of domains on viruses’ capsids.
Another example is the development of a nature-inspired stamping
technique able to transfer DNA patterns from a surface onto another.
This method has been tailored for the efficient production of
inexpensive DNA micro- and nano-arrays. A special emphasis in the group
is placed on the understanding of the nanoscale limitation of present
thermodynamic modeling of surface interactions.

Selected Publications

“Spontaneous assembly of sub-nanometre ordered
domains in the ligand shell of monolayer protected nanoparticles”,
Jackson, A. M.; Myerson, J. W.; Stellacci, F. Nature Materials,
3, 330-336, 2004.

“Supramolecular Nano-stamping: using DNA as
movable type”, Yu, A. A.; Savas, T. A.; Taylor G. S.; Guiseppe-Elie A.;
Smith H. I.; Stellacci F., Nano Letters, 5, 1061-1066,
2005.

“From Homo-Ligand to Mixed-Ligand Monolayer
Protected Metal Nanoparticles: a Scanning Tunneling Microscopy
Investigation”, Jackson, A. M.; Hu, Y.; Silva, P.; Stellacci F., J.
Am. Chem. Soc., 128, 11135–11149, 2006.

“Divalent Metal Nanoparticles”, DeVries, G. A.;
Brunnbauer, M.; Hu, Y.; Jackson, A. M.; Long, B.; Neltner, B.; Uzun,
O.; Wunsch, B. H.; Stellacci, F., Science, 315, 358–361,
2007.

Giulio Natta
From Wikipedia, the free encyclopedia

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Giulio
Natta

Giulio
Natta

Born
26
February 1903(1903-02-26)
Imperia, Italy

Died
2 May
1979 (aged 76)
Bergamo,
Italy

Nationality
Italy

Fields
Organic chemistry

Institutions
Pavia University
University of
Rome La Sapienza
Politecnico di Torino

Alma
mater
Politecnico di Milano

Known for
Ziegler-Natta catalyst

Notable awards
Nobel Prize in Chemistry (1963)

Giulio Natta (26 February 1903 - 2 May 1979) was an Italian chemist
and Nobel laureate. He who won a Nobel Prize in Chemistry in 1963
with Karl Ziegler for work on high polymers.

Contents
[hide]

• 1 Biography
  • 1.1 Early years
  • 1.2 Career
  • 1.3 Personal life
• 2 References
• 3 External links

//
[edit] Biography
[edit] Early years

Natta was born in Imperia, Italy. He
earned his degree in chemical engineering from the Politecnico di Milano university in Milan in
1924. In 1927 he passed the exams for becoming a professor there. In
1933 he became a full professor and the director of the Institute of
General Chemistry of Pavia University, where he stayed
until 1935. In that year he was appointed full professor in physical
chemistry at the University of
Rome.

[edit] Career

From 1936 to 1938 he moved as a full professor and director of the
Institute of Industrial Chemistry at the Polytechnic Institute
of Turin. In 1938 he took over as the head of the Department of chemical engineering at the Politecnico di Milano university, in a
somewhat controversial manner, when his predecessor Mario
Giacomo Levi was forced to step down because of racial laws
against Jews being introduced in Fascist
Italy.

Natta's work at Politecnico di Milano led to the improvement of
earlier work by Ziegler and to the development of the Ziegler-Natta catalyst. He received
the Nobel Prize in Chemistry in 1963
with Karl Ziegler for their research in high polymers.

Michele Ciavarella, http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
blogs http://rettorevirtuoso.blogspot.com/
YouTube Channel http://www.youtube.com/user/RettoreVirtuoso

There are other Italian Nobel Prize winners since Natta, both male and female.

Katia & Roberto

there were a few in science of italian origins but working abroad of course (like it would be your case Katia and Roberto if you manage to be lucky!), but noone like Natta who was working in Italy.  Actually Natta is the single one in Chemistry ever!

There are, viceversa, a few in literature, working in Italy.  Notice the case of W.D. Phillips of italian origins, and sharing the Nobel prize with Steven Chu present Energy Minister with Obama....   Since it seems extremely difficult to have Carlo Rubbia as Minister of Energy of Berlusconi, despite his innovation in Energy is very interesting, at least we could have been luckier to have Phillips with Obama!

So good luck with Nobel from Negative poisson's ratio.  Which area could that be Physics or Chemistry or Medicine?

PHISICS

Carlo Rubbia     1984     "for their decisive contributions to the large project, which led to the discovery of the field particles W and Z, communicators of weak interaction" Rubbia shared the prize with Simon van der Meer.

William D. Phillips     1997     "for development of methods to cool and trap atoms with laser light"
Phillips shared the prize with Steven Chu and Claude Cohen-Tannoudji.

Riccardo Giacconi     2002     "for pioneering contributions to astrophysics, which have led to the discovery of cosmic X-ray sources"Giacconi received half of the prize while Raymond Davis Jr. & Masatoshi Koshiba each received 1/4 of the prize.

MEDICINE

Salvador E. Luria     1969     "for their discoveries concerning the replication mechanism and the genetic structure of viruses"
Luria shared this award with Max Delbrück and Alfred D. Hershey.

Renato Dulbecco     1975     "for their discoveries concerning the interaction between tumour viruses and the genetic material of the cell" Dulbecco shared this award with David Baltimore and Howard Martin Temin.

Rita Levi-Montalcini     1986     "for their discoveries of growth factors" Levi-Montalcini shared this award with Stanley Cohen.

Louis J. Ignarro     1998     "for their discoveries concerning nitric oxide as a signalling molecule in the cardiovascular syste"
Louis J. Ignarro shared this award with Robert F. Furchgott and Ferid Murad.

Mario R. Capecchi     2007     "for their discoveries of principles for introducing specific gene modifications in mice by the use of embryonic stem cells" Mario R. Capecchi shared this award with Sir Martin J. Evans and Oliver Smithies.

LITERATURE
Eugenio Montale     1975     "for his distinctive poetry which, with great artistic sensitivity, has interpreted human values under the sign of an outlook on life with no illusions"

Dario Fò     1997     "who emulates the jesters of the Middle Ages in scourging authority and upholding the dignity of the downtrodden"

ECONOMIC

Franco Modigliani     1985     "for his pioneering analyses of saving and of financial markets"

Michele Ciavarella, http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
blogs http://rettorevirtuoso.blogspot.com/
YouTube Channel http://www.youtube.com/user/RettoreVirtuoso

Dear Katia,

Nice for you to have brought this up on iMechanica. 

I work on materials with negative Poisson's ratios (NPR) and negative thermal expansivity (NTE), and it's true that whenever I have what I think is a new idea I go to check Rod Lakes' web page.  More often than not I find Rod has done it and published it.... hey ho.

I like your recent work on symmetry breaking. Would you say that breaking of symmetry is neccessary for NPR ? (Am I right in thinking I can draw a honeycomb structure with a negative Poisson's ratio of -1 that does not change its symmetry ?) What do you think that  looking at symmetry tells you ? - I'm trying to explore your motivations here.

A significant technical hurdle that remains for NPR materials is their generally low stiffness. Making stiff materials with NPR has eluded everyone so far (to my knowledge). Is there a fundamental reason why this should be so ? (I think there might be). For instance, might you be able to design a fibrous composite which has both high stiffness and NPR via symmetry breaking ? (NPR composites from funny stack sequences have been around for a while but they're all low stiffness).

Nachiket above makes an interesting point about defects in structures that's close to my heart. We have been making NPR mateirals for some time, and some are very homgenous - honeycombs for instance, whereas others were very heterogeneous- foams for instance. We started to wonder how disorder affected Poisson's ratio, and in fact whether it is possible to deliberately use disorder to convert an otherwise+ve Poisson's ratio to -ve. It turns disorder has a strong affect upon Poisson's ratio and it can (probably) be used to generate -ve values 1, 2. Other publications by Neil Gaspar and Curt Koenders also explore this issue from a granluar mechanics standpoint. One thing that has emerged is that adding a small amount of disorder into an otherwise regular structure tends to generate effective structures of far larger scale than the starting base repeating unit. We're looking at some microCT data of deforming NPR foams to see if we can measure this effective structural size.

Concerning NTE - we looked at all the work on NTE and worked out that most if not all of the proposed structures exhibiting NTE could be described as colelctions of hinging or flexing beams. We then wrote down what we think are the base equations for such systems which if you know the geometry and constituent materials of such systems you can use to predict over all CTEs 3. Interestingly CTE is unbounded (a point first made by Rod Lakes) and very large +ve or -ve values are relatively easy to generate.

However many structures proposed for NTE are not stiff or are not weight efficient, something we're trying to investigate. Steeves in his recent JMPS paper addresses the issue of stiffness very well. Certainly the key questions I've been asked by industry on this subject have been about stiffness/strength and weight.

 1. Gaspar N, Smith CW, Behne EA, Seidler GT, and Evans KE, (2005b) “Quantitative Analysis of the Microscale of Auxetic Foams”, Physica Status Solidi b, 242/3, no. 05, pp 550-560.

2. Gaspar N, Smith CW, Evans KE (2003) “The effect of heterogeneity on the mechanical response of auxetic materials", Journal of Applied Physics 94 (9): pp. 6143-6149.

3. Miller W, Mackenzie DS, Smith CW, Evans KE (2008) “A Generalised Scale-independent Mechanism for Tailoring of Thermal Expansivity; Positive and Negative” Mech of Mat, 40, pp 351-361

Chris

Prof Chris Smith,
Associate Professor in Functional Materials School of Engineering, Computing
and Mathematics, University of Exeter, Exeter, Devon, EX4 4QF, UK.
tel +44 (0) 1392 263652, fax +44 (0) 1392 217965
http://www.secam.ex.ac.uk/profile/cwsmith

Katia,

 I am also curious about the stiffness of npr materials.  What are typical values of the modulus?  In the current state of npr materials, could they even be used in applications such as opening (fairly compliant) blood vessels?

Thanks,
Matt

This is the way forward, keep thinking and speculating of applications!  This is the way imechanica is a nice forum in the old sense of Greek and Latin philosophers "forum -- is a latin word " like in the Roman Empire

The Roman Forum, also known by its original Latin designation (Latin: Forum
Romanum, Italian: Foro Romano),
is located between the Palatine
Hill and the Capitoline Hill of the city of Rome, Italy.
Citizens of the ancient city referred to the location as the "Forum
Magnum" or just the "Forum". 

The Forum Romanum. View facing North East from above the Portico Dii Consentes.

 Sorry for the digression, but being Katia, Roberto Ballarini and myself, italian, I became a little patriotic today in this forum!!  :)

Michele Ciavarella, http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
blogs http://rettorevirtuoso.blogspot.com/
YouTube Channel http://www.youtube.com/user/RettoreVirtuoso

Dear Prof Ballarinia - your paper sounds very interesting. Perhaps I'm being stupid but which paper do you refer to  ? (I could not see you as an author in any of the papers Prof Bertoldi cites)

Am I right in thinking your argument about 'continuity in space' as being about density? I can't do it now but a survey of NPR materials on a density specific stiffness basis would be revealing. My feeling is they will probably still not compare well.

Prof Bertoldi does have a point, that most NPR materials studied to date have been inherently low modulus. I wonder though if we consider things on a relative basis, do NPRversions have lower moduli values than normal positive PR versions ?

Does anyone know the modulus of the CNT sheets? (My scan of the paper doensn't seem to reveal any).

Fatigue - I would tend to agree that the deformation mechanism leading to NPR (internal rotations) ought to lead to stress concentrations and thus low fatigue life. The only work I know on this is by Fabrizio Scarpa (Bristol) who, if memory serves, found enhanced lifetimes vs conventional versions. Hey ho...

Chris

Prof Chris Smith,
Associate Professor in Functional Materials School of Engineering, Computing
and Mathematics, University of Exeter, Exeter, Devon, EX4 4QF, UK.
tel +44 (0) 1392 263652, fax +44 (0) 1392 217965
http://www.secam.ex.ac.uk/profile/cwsmith

Dr Scarpa is a member of the Aerospace Composites research group. His principal research interests are listed below.

Auxetic structures

Auxetic solids feature a negative Poisson's ratio (NPR) effect, expanding in all directions when pulled in only one. We design and manufacture cellular materials with auxetic characteristics to enhance the structural integrity, vibroacoustic signature and electromagnetic properties of novel concept of sandwich structures. Current programs involve also the design of NPR honeycombs cells with embedded MEMS for structural health monitoring and active electromagnetic compatibility. Cellular structures with NPR capabilities are also used to design novel concepts of morphing airfoils with continuous camber variation.
Sponsors: EPSRC, EU FP6, DTI, US Army ARO, QinetiQ plc

Passive and active NPR foams

We have modelled and manufactured samples of negative Poisson’s ratio foams using alternative production procedures from the ones illustrated in literature. Work on the area has focused on static and dynamic performance of mechanical properties, crashworthiness capabilities and absorption acoustic properties. Further studies have been carried out also on auxetic and conventional PU foams doped with magnetorheological fluid – both mechanical, acoustic and dielectric properties showed significant changes when loaded with external magnetic fields.
Sponsors: EPSRC, Royal Society, DTI HEFCE, British Vita plc, Xetal ltd

Shape memory alloy honeycombs

We have developed conventional and auxetic honeycombs made of 1 and 2 ways shape memory alloy material. The cellular structures provide changes of stiffness with temperature loading. Large recoverable deformations can be obtained, as well as increased damping capacity under random vibration excitation. The cores can be used in sandwich structures for crashworthiness applications and in satellite-type antennas with deployability capabilities.
Sponsors: EPSRC, US Army ARO

Analysis tools

We have developed numerical techniques to improve the vibroacoustic prediction of sandwich and smart structures in middle and high frequency domains, using Spectral Finite Elements or wavelet-based condensation techniques on classical FEM models. Damping characteristics of sandwich structures with viscoelastic material inserts are also simulated with numerical methods improving the initial estimate given by the Modal Strain Energy method applied to classical FEM models. Recent work has focused on homogenisation numerical techniques and the use of metamodelling strategies with Genetic Programming and Artificial Neural Networks to reduce the computational costs for material of microstructure composite design.
Sponsors: EPSRC, Rolls Royce plc

Michele Ciavarella, http://poliba.academia.edu/micheleciavarella Editor, Italian Science Debate, www.sciencedebate.it blogs http://rettorevirtuoso.blogspot.com/ YouTube Channel http://www.youtube.com/user/RettoreVirtuoso

Did you conclude anything worth pursuing?

Michele Ciavarella, http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
blogs http://rettorevirtuoso.blogspot.com/
YouTube Channel http://www.youtube.com/user/RettoreVirtuoso

Katia and al.

 I would lilke to add to the discussion a few of my own papers (joint with F. Scarpa and other authors) which show interesting phononic properties of auxetic lattices:

 A. Spadoni, S. Gonella, F. Scarpa, “Phononic Properties of Hexagonal Chiral Lattices” Wave Motion, Volume 46, Issue 7, November 2009, Pages 435-450

 Ruzzene M., Scarpa F., 2005 “Directional and Band-Gap Behavior of Auxetic Lattices.” Physica Status Solidi B, 242, No. 3, 665–680

Ruzzene M., Soranna F., Scarpa F., 2003 “Wave Beaming Effects in Bi-Dimensional Cellular Structures.”, Smart Materials and Structures, 12, pp. 363-372 

Such properties include band gaps and directionality (wave beaming), which can be related to the anisotropic properties of re-entrant lattices, and to the unique deformation mechanism of chiral lattices. A direct relation between NPR and interesting phononic (wave guiding) properties is still missing.

Regarding possible applications of auxetic lattices (without a clear connection with NPR yet, here again):

 Ruzzene M., 2004 “Vibration and Sound Radiation Of Sandwich Beams With Honeycomb Truss Core.” Journal of Sound and Vibration, 277(2004), pp.741-763.

Scarpa F., Blain S., Lew T., Perrott D., Ruzzene M., and Yates J. R., 2006 “Analytical And Experimental Analysis On The Elastic Buckling Of Hexagonal Chiral Cell Honeycombs” Composites Part A: Applied Science and Manufacturing Volume 38, Issue 2 , February 2007, Pages 280-289

Spadoni A., Ruzzene M., 2006 “Static Aeroelastic Response of Chiral Truss-core Airfoils” Journal of Intelligent Material Systems and Structures, 5 2007.

Michele Ciavarella, http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
blogs http://rettorevirtuoso.blogspot.com/
YouTube Channel http://www.youtube.com/user/RettoreVirtuoso

Here is the structure of a 3D auxetic periodic material that uses rotating regular octahedra, from Adrian Rossiter's website, showing how also in this case stress concentration is necessary to achieve NPR. This is somewhat similar to the 2D lattice of connected rotating squares.

http://www.antiprism.com/misc/jit_cubo_oct3b.gif

http://www.antiprism.com/misc/jit_cubo_oct3c.gif

http://www.antiprism.com/misc/jit_cubo_oct4.gif

http://www.antiprism.com/misc/jit_cubo_oct4c.gif

All the animations refer to the same structure, the only difference is size and relative motion between bodies. Ignore the attachment/detachment of the vertices during the animation, this is only due to final and initial configurations being identical. Note that the auxetic behaviour is still 2D. Looking carefully, it is possible to spot the global rotational axis. There is no strain along this direction. Considering the fully open configuration, axis Miller indices are [111]. Contractions/expansions take place on its related plane, which is orthogonal to the axis.

Looking even more carefully, only two types of octahedra can be seen, rotating in opposite directions each other.

Although one might be led to think of a global torsional component, this is not present. Each octahedron, excluding those pierced by the rotational axis, moves only radially from its initial position to the outermost position (fully open configuration) and back to tightly pack closer to the axis. This is best shown in the third animation, where the octahedra pierced by the rotational axis are counter-rotating.

Auxetic components of this kind can be manufactured using a Schwarz P surface as a template, and cutting it between two parallel [111] planes.

For a reference on the better-known example of rotating squares, check this article.

Auxetic behavior from rotating squares. J. N. Grima and K. E. Evans., J. Mat. Sc. Lett., Vol. 19(17), 1563-1565

-- Ruggero Gabbrielli

Can we hang on to using English for a moment?

Perhaps it would help to list the groups active in research on NPR and its effects ?

So apart from those people who have already disclosed their interests so far in this thread, I know of  the following groups/people -

Anselm Griffin (Georgia Tech, USA)

Andy and Kim Alderson (Bolton Univ, UK)

Fabrizio Scarpa (Bristol, UK)

Krzysztof Wojciechowski  (IFM-PAN, Poznan, Poland)

Joseph Grima (Chemistry, Malta)

The order implies nothing, and I accept any blame for ommissions. Please feel free to add to this if you see an ommission.

Would a similar list for materials / structures with negative or unusual CTE be of interest to people ? (The trouble is this would include a lot of chemists and physicists who make/study materials with funny CTE).

I attempted to review this area recently in a paper in Journal of Materials Science (Journal of Materials Science 44 5441-5451 [DOI 10.1007/s10853-009-3692-4]) but I know it's already out of date.

Chris

Prof Chris Smith,
Associate Professor in Functional Materials,
College of Engineering, Mathematics & Physical Sciences, University of Exeter, UK.
tel
http://www.secam.ex.ac.uk/profile/cwsmith

I see the discussion has gone into anisotropic material properties now.  It is all interesting, but every now and then, I need to know where we are aiming at.  I am still confused about applications.  Maybe Katia can help :=)

Michele Ciavarella, Politecnico di BARI - Italy, Rector's delegate.
http://poliba.academia.edu/micheleciavarella
Editor, Italian Science Debate, www.sciencedebate.it
Associate Editor, Ferrari Millechili Journal

I'll try to offer up some suggested applications, and Katia et al can correct my mistakes & ommissions...

I'll also point Mike and others at two reviews i) in 2004 by Yang et al in J Mat Sci (vol 30, page 3269), and ii) by Evans and Alderson in Adv Mat in 2000 (vol 12, page 617).

It might be helpfull to divide up applications into those directly associated with the negative Poisson's ratio effect, and those arising indirectly from it.

Direct applications.

Composites with auxetic fibres might show high toughness or be able to use shorter fibres because  the auxetic fibres have higher frictional losses during pull out (they lock themselves into their cavities under tension). Such fibres may acts as balancing plies during manufacture because they may effectively reduce thermal expansivity (see recent papers and patents by Alderson). Negative Poisson's ratio in plane may also make draping of prepregs easier because they will naturally form synclastic curvatures (dome shapes) as opposed to anticlastic curvatures (saddle shapes) like positive PR versions.

Some other claims and verifications have been published for fracture toughness in compsoites with various NPRs. I'm not sure there is a large body of evidence for this and this is obviously an interesting avenue of work for someone.

Indentation. since auxetic material underneath a point load (in compression) will tend tomove inwards towards the line of compression rather than away form it as with a PPR material, the resistance to indentation tends to be higher and different with auxetics. This is a nice example of a smart materials response - localised stiffening. I see no reason why such benefits woudl not be seen at high strains rates also, eg for crash protection.

However this response is also in part a result of the increased shear modulus associated with NPR - that is for a given value of Young's moudulus, a NPR below -0.5 will engender a larger shear modulus. As you'll see from the relationship between these elastic constants if nu tends to -1 the shear modulus rises to infinite. Thus Poisson's ratio is a nice way to decouple Young's and shear moduli.

Tunable Deformation. Since the PR controls all deformations in axes other than that applied it offers a large degree of control over how a structure interacts with other structures or fluids. Applications seem possible in aerospace, marine atuomotive and locmotive applications where a particular structural response can be encodedinto astructure via PR especially if it is possible to functionally grade it across a structure.

Indirect applications.

These arise because PR has an influence on other properties or because the microstructure leading to NPR engenders other effects. For example I think both Rod Lakes and Fabrizio Scarpa (and possibly others) have deomonstrated improved acoustic absorption and viscoelastic loss in NPR foams and honeycomb sandwich panels, though in the case of the foams this was probably due to the more tortuous microstructure of the foams than any elastic property per se. We have done some nice work with Fabrizio Scarpa recently on vibration damping in NPR honeycombs which we expect to publish soon.

It has also becaome apparent that there are many advantages in NPR materials as hosts for ElectroMagnetic (EM) active inclussions, usually metallic objects. Control over deformation behaviour in plane in say a honeycomb, allows control over spacing and orientation of EM active elements and thus functionaliies such as absorbtion/relfection, beam steering, wave compression, etc. Perhaps most of this work has so far been done by Fabrizio Scarpa, though I have some ongoing in my laboratory at present. Interstingly, closely related resonance phenomena have been demonstrated for acoustic waves by Massimo Ruzzene (have a look at his webpage for a gorgeous example of beam steering in a chiral NPR honeycomb - http://www.me.gatech.edu/faculty/ruzzene.shtml).

NPR solids such as foams or honeycombs may also have application as separators for particles in fluids. With PPR solids it is possible only to clsoe down pores, but with NPR solids it is possible to open up pores as well. This could have some significant benefits over current filtration systems which usually have to be clsoed down for cleaning or replacement of filters. NPR filters could be cleaned in situ.

There has been some investigation of the benefits of using NPR materials in Piezoceramic composites. 

I'm sure I've missed several issues here, so please feel free to point out errors or ommissions.

Chris

Prof Chris Smith,
Associate Professor in Functional Materials,
College of Engineering, Mathematics & Physical Sciences, University of Exeter, UK.
tel
http://www.secam.ex.ac.uk/profile/cwsmith

From Adrian: 

The first is a "rotating cubes" model, which is like the
"rotating octahedra", but uses cubes and the rotating
squares transformation

  http://www.antiprism.com/misc/squ_jit_cubes01.gif

It looks familiar, but I am not sure from where.

I saw that the cubes could be augmented to form a packing
of rhombic dodecahedra, and these could be used in the
transformation instead

  http://www.antiprism.com/misc/squ_jit_rd01.gif

However, the rhombic dodecahedron can also be formed by
augmenting the octahedron, and the original "rotating
octahedra" transformation can also be modelled with rhombic
dodecahedra. These pack as before, but are connected
differently

  http://www.antiprism.com/misc/tri_jit_rd01.gif

Adrian
-- Adrian Rossiter
adrian@antiprism.com
http://antiprism.com/adrian

Hi all,

 Does anyone know how to model the regaular foam as a auxetic foam using ls-dyna?which material card is used and what kind of  element type must be selected?

 Thanks in advance.

Karthik 

I wonder if there's been any work in analyzing defects in  metamaterials kidney stones