# Difference between revisions of "Poisson's Ratio"

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− | + | ==Definition== | |

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+ | When a material is elongated or compressed along one axis, the Poisson's ratio, <math>\nu</math>, of a material is the ratio of the [[Strain]] in the directions perpendicular to the axis, divided by the [[Strain]] along that axis. Essentially, this dimensionless number describes the tendency of a contraction or expansion in one dimension to cause contraction or expansion in other dimensions. Most materials have a positive Poisson's ratio, meaning other dimensions will contract in response to elongation along one dimension, and vice versa. Most materials have a Poisson's ratio near 0.3, with more rubbery materials approaching 0.5. [3] Materials with negative Poisson's ratio were first reported in 1987 by Lakes. Example materials of this type include some foams, honeycomb structures produced by Prall and Lakes,[3] and patterned arrays of circular and elliptical holes in an elastomer (Bertoldi).[3] In these last two cases, local buckling of the structure walls leading to volume reduction is directly observed to cause a negative Poisson's ratio. Figure 1 shows a schematic of local buckling in Bertoldi's material. | ||

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+ | ''Important Limits'' | ||

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+ | For an isotropic, unconstrained three dimensional elastic material, Poisson's ratio must range from -1 to 1/2.[3] | ||

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+ | ==References== | ||

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+ | [1]http://silver.neep.wisc.edu/~lakes/PoissonIntro.html | ||

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+ | [2] '"Negative Poisson’s Ratio Behavior Induced by an Elastic Instability". Katia Bertoldi, Pedro M. Reis, Stephen Willshaw, and Tom Mullin. ''Adv. Mater''. 2009, 21, 1–6. | ||

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+ | [3] "Properties of a chiral honeycomb with a Poisson's ratio -1" D. Prall, R. S. Lakes. ''Int. J. of Mechanical Sciences'', 39, 305-314, (1996) | ||

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==Keyword in References== | ==Keyword in References== | ||

[[Homogeneous flow of metallic glasses: A free volume perspective]] | [[Homogeneous flow of metallic glasses: A free volume perspective]] |

## Revision as of 15:41, 10 December 2011

## Definition

When a material is elongated or compressed along one axis, the Poisson's ratio, <math>\nu</math>, of a material is the ratio of the Strain in the directions perpendicular to the axis, divided by the Strain along that axis. Essentially, this dimensionless number describes the tendency of a contraction or expansion in one dimension to cause contraction or expansion in other dimensions. Most materials have a positive Poisson's ratio, meaning other dimensions will contract in response to elongation along one dimension, and vice versa. Most materials have a Poisson's ratio near 0.3, with more rubbery materials approaching 0.5. [3] Materials with negative Poisson's ratio were first reported in 1987 by Lakes. Example materials of this type include some foams, honeycomb structures produced by Prall and Lakes,[3] and patterned arrays of circular and elliptical holes in an elastomer (Bertoldi).[3] In these last two cases, local buckling of the structure walls leading to volume reduction is directly observed to cause a negative Poisson's ratio. Figure 1 shows a schematic of local buckling in Bertoldi's material.

*Important Limits*

For an isotropic, unconstrained three dimensional elastic material, Poisson's ratio must range from -1 to 1/2.[3]

## References

[1]http://silver.neep.wisc.edu/~lakes/PoissonIntro.html

[2] '"Negative Poisson’s Ratio Behavior Induced by an Elastic Instability". Katia Bertoldi, Pedro M. Reis, Stephen Willshaw, and Tom Mullin. *Adv. Mater*. 2009, 21, 1–6.

[3] "Properties of a chiral honeycomb with a Poisson's ratio -1" D. Prall, R. S. Lakes. *Int. J. of Mechanical Sciences*, 39, 305-314, (1996)

## Keyword in References

Homogeneous flow of metallic glasses: A free volume perspective