# Materials with Zero Poisson Ratio

Poisson's ratio is defined as negative ratio between transverse and axial strain. So, a material with zero poisson ratio must necessarily exhibit no transverse strain. After checking the wikipedia, I was suprised to discover that a CORK has a near-zero poisson ratio. I haven't found any references yet to other materials that also have zero poisson ratio.

What is so special about a cork that produces its zero poisson ratio? What other materials share this characteristic?

• Do you mean the stuff from a cork tree or synthetic material used to manufacture bottle stoppers. – Mark Rovetta Jun 18 '13 at 14:36
• see this tough reference page 355 - Mechanical properties – Trimok Jun 18 '13 at 16:02
• "So, a material with zero Poisson ratio must necessarily exhibit no transverse strain" That is not true. You forgot about half the definition of Poisson's ratio - i.e. what is the stress field, when you measure the ratio of the two strains. – alephzero Feb 26 '19 at 14:19

It's no trick at all to obtain a Poisson ratio of nearly zero in a material in general; you just need to suppress any mechanisms that would produce a lateral expansion (or, much less typically, contraction) upon uniaxial compression.

If we remove material, for example, then we sidestep the issue—that we'd otherwise encounter—that uniform condensed matter tends to stay at a constant volume when it's deformed (particularly so for liquids and compliant solids). Cellular solids, however, i.e., solids with some missing regions (such as foams, honeycombs, cancellous bone, and cork) can easily deform uniaxially with negligible lateral deformation. Consider the uniaxial crushing of an aluminum honeycomb as an extreme example in which a cellular solid easily accommodates densification:

Papka, Scott D., and Stelios Kyriakides. "In-plane compressive response and crushing of honeycomb." Journal of the Mechanics and Physics of Solids 42.10 (1994): 1499-1532.

An excellent general reference on this topic is Gibson and Ashby's Cellular Materials; in fact, the authors begin by describing Robert Hooke's ca. 1660 observations of the microscopic structure of cork, a type of oak bark:

Micrographia (1665) https://www.nlm.nih.gov/exhibition/hooke/images/cork1.jpg

(Such observations ultimately led to the term "cell" for the proliferating biological unit of life, as the spaces reminded Hooke of a monk's monastery cell.)

Micrographs of cork from a modern scanning electron microscope strongly resemble Hooke's sketches:

Fortes, M. A., and M. Teresa Nogueira. "The Poisson effect in cork." Materials Science and Engineering: A 122.2 (1989): 227-232. Left image shows a section parallel to the radial direction, revealing staggered cell closures separated by corrugated walls. Right image looks down the radial direction, showing approximately hexagonal divisions.

It's useful to refer to the conventional coordinate system:

Gibson, Lorna J., and Michael F. Ashby. Cellular Solids: Structure and Properties. Cambridge university press, 1999.

The cork cells are closed, roughly hexagonal cells (as viewed down the radial direction) with corrugated walls (as viewed in the axial or tangential directions) that collapse easily under load. As a result, Poisson's ratio involving the radial direction is very small and nearly zero because the solid material simply folds up into the existing adjacent spaces. (Other related outcomes are that Young's modulus and the bulk modulus are low, the density is low, the thermal conductivity is low, and the loss coefficient is high, as is the energy absorption capacity.)

Greaves et al.'s review article on Poisson's ratio $$\nu$$ plots this parameter against the ratio of the bulk modulus $$B$$ to the shear modulus $$G$$:

Greaves et al. "Poisson's ratio and modern materials." Nature Materials 10.11 (2011): 823.

As expected (and as discussed in Gibson and Ashby's textbook), we find that other cellular materials such as honeycombs and auxetic materials with reentrant structures share the $$\nu\approx 0$$ space adjacent to cork.

• So it’s not so much a fundamental property of the material itself that gives it a zero Poisson ratio... it’s just the way is layed out allows for space to “absorb” lateral deformation. It has been years since i asked this question and since then i realized that my mistake was believing that the poisson ratio applied to the uniform condensed matter, not the bulk matierial with void spaces. – Paul Feb 28 '19 at 1:52