## Poisson's ratio greater than 1

## Poisson's ratio greater than 1

(OP)

Dear all,

I am looking for references, most likely relating to laminated materials, that discuss Poisson's ratios greater than 1. I'm especially interested in proofs on any type. I know that we can easily prove that for isotropic incompressible materials, that the poisson's ratio can't be greater than 1, but what about for other non-isotropic materials?

-ldp

I am looking for references, most likely relating to laminated materials, that discuss Poisson's ratios greater than 1. I'm especially interested in proofs on any type. I know that we can easily prove that for isotropic incompressible materials, that the poisson's ratio can't be greater than 1, but what about for other non-isotropic materials?

-ldp

## RE: Poisson's ratio greater than 1

## RE: Poisson's ratio greater than 1

For a 2D "material" like a sheet of honeycomb core, for hexagonal cells the poisson's ratio is 1.0 in both the 12- and 21-directions. If you stretch the core sideways ("over expanding" it), the cells become more rectangular. When the cells are exactly rectangular, the theoretical poisson's ratio is 0 in the 12-direction and infinity in the 21-direction... For a cell shape which deviates from rectangular (90 degree internal angles) by 5 degrees the theoretical 21 poisson's ratio is about 10.5. It's similar at the other extreme: for "under expanded" honeycomb cells, with internal angles 90, 135, 135, 90, 135, 135, the 12-direction theoretical poisson's is 2.41 (actually root(2) + 1). For completely unexpanded core the 12-direction poisson's is infinite while the 21-direction is zero. I have a little Excel 97 spreadsheet illustrating honeycomb core poisson's ratios for different cell shapes that I can e-mail you if you post an e-address.

It is also possible to manufacture 2D "materials" like this with very large negative poisson's ratios. You have to manipulate the cells so that they all become sort of 'X'-shaped.

All these effects rely on the "material" having a microstructure (macrostructure, really, in the case of honeycomb core) which behaves as a mechanism. 3D materials are possible, but get more complicated. Coming up with what we would regard as actual materials with such properties is trickier. I remember an article in Nature in either 1993 or 1994 which featured negative and unusual poisson's rations in single-crystal metallic materials. However, from memory the poisson's were highly anisotropic. More recent stuff can be found from entering auxetic into the search box at http://www.nature.com/nature/ .

There's also some fascinating stuff about materials with a phase having negative stiffness at http://silver.neep.wisc.edu/~lakes/NegStf.html , though for "with a phase" something like "including micro-mechanisms" might be more appropriate.

Thought for the day: if you mix equal amounts of positive and negative stiffness "materials" together, the flexibilities cancel out and (for just an instant) you have something with theoretically infinite stiffness...

-R.

## RE: Poisson's ratio greater than 1

Thanks for your help. I had looked at that (yours?) web site earlier and found it very interesting. I am looking to advance some theories for "solid" materials. My interest in high Poisson's ratios comes from my work with fiber-reinforced elastomers. The only solid references relating to high poisson's ratios I have been able to come up with is "Microstructural Design of Fiber Composites" by Chou, and some geo-tek or soils-related papers. The web site you suggested has given me some ideas, perhaps I will have to consider Hooke's law using a full anisotropic stiffness matrix. If you are familiar with composites (classical lamination) theory, you know that we can get v12 = Qbar12/Q22, and plot the poisson's ratio as a function of fiber angle for any orthotropic material. What I would like to do, is determine theoretical limits for say v12 as a function of oriented orthotropic material properties and fiber angle, much like we can prove that for an incompressible isotropic solid (rubber) v or Poission's ratio will be 1/2. I keep thinking that I am missing something obvious.

take care,

orangepeel

PS..... I have just read your posting again.... and there may be more correlation between your high poisson's ratios, and what I am seeing, than I originally thought. This requires some more pondering. In the mean time, I would like to have you email me the excel file you mentioned, to kfldp00@tamuk.edu.

## RE: Poisson's ratio greater than 1

Can u point out a site for application of negative poisson's ratio materials for textiles.With regard to manufacture,properties and uses etcetc

## RE: Poisson's ratio greater than 1

and i also had a basic question .

in a positive honey comb strcuture when extended the area would remain the same i suppose since the overall perimeter remains same.For a negative poissons auxetic material ,under stretch the material expands in all directions,how does this influence the overall area and volume of air contained in it.

## RE: Poisson's ratio greater than 1

I am not aware of any such web sites for textiles, on the honeycomb question, you might have better luck posting it as a separate topic. I can't claim any significant expertise on deformed honeycomb structures.... Perhaps RPstress might be able to help.

Good luck!

## RE: Poisson's ratio greater than 1

Attempt at graphic in fixed pitch:

A. B.

^^^^^^^^^^^^^^^^^^^^^^^^ PULL!

|| ||

|| ||

|| || ____||____ ____||____

|\ || /||\ || /| | || |

| \||/ || \||/ | | || |

| || | | || |

| /||\ || /||\ | | || |

|/ || \||/ || \| |____ ____||____ ____|

|| || || || \ somehow make

|| || \___ these bits rigid.

|| ||

vvvvvvvvvvvvvvvvvvvvvvvv PULL!

As can be seen from the above "diagram", the area and perimiter both increase. For a flat "material" such as a honeycomb, the area changes for any cell shape other than hexagonal (all internal angles 120 deg). For a 2D material, no change in area means a poisson's of 1.0.

[Also, note that for these sorts of pure mechanisms, stiffnesses and stresses are nominally zero and "poisson's" is the ratio of strains. For actual solid materials, poisson's relates the stress in one direction to the strain in others.]

Bias-cut cloth is renowned for its "clinginess". As opposed to negative poisson's, what you might achieve with an ultra-high positive poisson's material I don't know...is this how fishnet stockings work?

## RE: Poisson's ratio greater than 1

I know some work was done in this area in the development of nonwoven materials (nylon). There was considerable effort to make a material/composite that could be used as a reinforcing material for tires.

I do remember that they made thick multilayer products with both random/random, random/bias, combinations of others materials in the layers. There were always discussions of the directional properties in the terms you discussed. They only thing that I’ve seen come close to these materials in appearance is the 3M pads.

I was involved in the mechanical end and didn’t stay around for these discussions, whish I had now.

I don’t think anything was published.

There is some interesting reading around concerning the use of honeycomb material as shock absorbers.

## RE: Poisson's ratio greater than 1

I read professor lakes site on Auxetics

(http://silver.neep.wisc.edu/~lakes/Poiss...) and application of Auxetics in textiles in http://research.dh.umu.se/dynamic/artikl.....

In the first,there was a picture of open structured foam of small thickness which showed the change in size and shape of a auxetic material with stretch.This gave me the idea that perhaps auxetics could be used in functional textiles where vaiable coverfactor is required for functions such a smart moisture or thermal management.As Rpstress pointed out it might be difficult to implement due to the compressive properties of textiles.But perhaps Auxetic textiles would be realised in the future.

## RE: Poisson's ratio greater than 1

Back to high Poisson's ratios.......RPstress mentioned "fishnet" stockings, or perhaps something like an onion sack. That may be similar to what I am trying right now. Anyone else tried a scissoring net like that for structural purposes? What kind of structural response did you get?

thanks,

## RE: Poisson's ratio greater than 1

http://www.azom.com/details.asp?ArticleID=168