# Poisson's Ratio

When a sample of material is stretched in one direction it tends to get thinner in the lateral direction - and if a sample is compressed in one direction it tends to get thicker in the lateral direction.

** Poisson's ratio ** is

- the ratio of the relative contraction strain (transverse, lateral or radial strain) normal to the applied load - to the relative extension strain (or axial strain) in the direction of the applied load

Poisson's Ratio can be expressed as

μ = - ε_{ t }/ ε_{ l }(1)

where

μ = Poisson's ratio

ε_{ t }= transverse strain (m/m, ft/ft)

ε_{ l }= longitudinal or axial strain (m/m, ft/ft)

Strain is defined as "deformation of a solid due to stress".

** Longitudinal ** (or axial) strain can be expressed as

ε_{ l }= dl / L (2)

where

ε_{ l }= longitudinal or axial strain (dimensionless - or m/m, ft/ft)

dl = change in length (m, ft)

L = initial length (m, ft)

** Contraction ** (or transverse, lateral or radial) strain can be expressed as

* ε _{ t } = dr / r (3) *

* where *

* ε _{ t } = transverse, lateral or radial strain (dimensionless - or m/m, ft/ft) *

* dr = change in radius (m, ft) *

* r = initial radius (m, ft) *

Eq. 1, 2 and 3 can be combined to

*μ = - ( dr / r ) / ( dl / L ) (4) *

### Example - Stretching Aluminum

An aluminum bar with length * 10 m * and radius * 100 mm (100 10 ^{ -3 } m) * is stretched

*5 mm (5 10*. The radial contraction in lateral direction can be rearranged to

^{ -3 }m)* dr = - μ r dl / L (5) *

With Poisson's ratio for aluminum * 0.334 * - the contraction can be calculated as

* dr = - 0.334 ( 100 10 ^{ -3 } m ) ( 5 10 ^{ -3 } m) / (10 m) *

* = 1.7 10 ^{ -5 } m *

* = 0.017 mm *

### Poisson's Ratios for Common Materials

For most common materials the Poisson's ratio is in the range * 0 - 0.5 * . Typical Poisson's Ratios for some common materials are indicated below.

Material | Poisson's Ratio - μ - |
---|---|

Upper limit | 0.5 |

Aluminum | 0.334 |

Aluminum, 6061-T6 | 0.35 |

Aluminum, 2024-T4 | 0.32 |

Beryllium Copper | 0.285 |

Brass, 70-30 | 0.331 |

Brass, cast | 0.357 |

Bronze | 0.34 |

Clay | 0.41 |

Concrete | 0.1 - 0.2 |

Copper | 0.355 |

Cork | 0 |

Glass, Soda | 0.22 |

Glass, Float | 0.2 - 0.27 |

Granite | 0.2 - 0.3 |

Ice | 0.33 |

Inconel | 0.27 - 0.38 |

Iron, Cast - gray | 0.211 |

Iron, Cast | 0.22 - 0.30 |

Iron, Ductile | 0.26 - 0.31 |

Iron, Malleable | 0.271 |

Lead | 0.431 |

Limestone | 0.2 - 0.3 |

Magnesium | 0.35 |

Magnesium Alloy | 0.281 |

Marble | 0.2 - 0.3 |

Molybdenum | 0.307 |

Monel metal | 0.315 |

Nickel Silver | 0.322 |

Nickel Steel | 0.291 |

Polystyrene | 0.34 |

Phosphor Bronze | 0.359 |

Rubber | 0.48 - ~0.5 |

Sand | 0.29 |

Sandy loam | 0.31 |

Sandy clay | 0.37 |

Stainless Steel 18-8 | 0.305 |

Steel, cast | 0.265 |

Steel, Cold-rolled | 0.287 |

Steel, high carbon | 0.295 |

Steel, mild | 0.303 |

Titanium (99.0 Ti) | 0.32 |

Wrought iron | 0.278 |

Z-nickel | 0.36 |

Zinc | 0.331 |

## Related Topics

### • Mechanics

Forces, acceleration, displacement, vectors, motion, momentum, energy of objects and more.

### • Miscellaneous

Engineering related topics like Beaufort Wind Scale, CE-marking, drawing standards and more.

## Related Documents

### Malleability vs. Brittlenes vs. Ductility

Plastic deformation properties.

### Metals - Machinability

The machinability of some common metals.

### Metals and Alloys - Bulk Modulus Elasticity

The Bulk Modulus - resistance to uniform compression - for some common metals and alloys.

### Metals and Alloys - Young's Modulus of Elasticity

Elastic properties and Young's modulus for metals and alloys like cast iron, carbon steel and more.

### Modulus of Rigidity

Shear Modulus (Modulus of Rigidity) is the elasticity coefficient for shearing or torsion force.

### Poisson's Ratios Metals

Some metals and their Poisson's Ratios.

### Ratios and Proportions

The relative values between quantities - ratios and proportions.

### Stress, Strain and Young's Modulus

Stress is force per unit area - strain is the deformation of a solid due to stress.

### Young's Modulus, Tensile Strength and Yield Strength Values for some Materials

Young's Modulus (or Tensile Modulus alt. Modulus of Elasticity) and Ultimate Tensile Strength and Yield Strength for materials like steel, glass, wood and many more.