# Poisson's ratio

## When a material is stretched in one direction it tends to get thinner in the other two directions

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When a sample of material is stretched in one direction it tends to get thinner in the other two directions.

Poisson's ratio is the ratio of the relative contraction strain, or transverse 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

υ = - ε_{t}/ ε_{l}(1)

where

υ = Poisson's ratio

ε_{t }= transverse strain

ε_{l }= longitudinal or axial strain

Strain can be expressed as

ε = dl/L (2)

where

dl = change in length

L = initial length

For most common materials the Poisson's ratio is in the range *0 - 0.5*.

### Typical Poisson's Ratios for some Common Materials

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

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 |

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 |

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 |

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