MAT-32

Poisson ratio

ν = −εlat / εlong. Lateral contraction over axial stretch.

Reading speed

ElasticityPoisson 1827

Governing equation

\nu=-\varepsilon_{\mathrm{lat}}/\varepsilon_{\mathrm{long}}

where

\varepsilon_{\mathrm{lat}}: Lateral strain (—)
\varepsilon_{\mathrm{long}}: Axial strain (—)
\nu: Poisson ratio (—)

Lecture brief

Historical brief

Hooke (1678), Hall–Petch grain size, Arrhenius activation and Paris fatigue-crack growth are the spine of materials selection. The sheets relate stress, microstructure and life. This sheet (MAT-32 — Poisson ratio) is the form associated with Poisson 1827. Working symbols: $\varepsilon_{\mathrm{lat}}$ , $\varepsilon_{\mathrm{long}}$ $\rightarrow$ $\nu$ . Poisson's ratio is a thermodynamic elastic constant. For isotropic solids −1 < ν < 0.5, with 0.5 the incompressible limit.

Purpose

Purpose: compute

\nu

from

\varepsilon_{\mathrm{lat}}

\varepsilon_{\mathrm{long}}

in Materials via

\nu=-\varepsilon_{\mathrm{lat}}/\varepsilon_{\mathrm{long}}

ν = −εlat / εlong. Lateral contraction over axial stretch. Use it when a real materials question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\varepsilon_{\mathrm{lat}} = -3.000e-4\,\mathrm{—}

\varepsilon_{\mathrm{long}} = 0.001\,\mathrm{—}

, the governing relation

\nu=-\varepsilon_{\mathrm{lat}}/\varepsilon_{\mathrm{long}}

yields

\nu = 0.300\,\mathrm{—}

. A stretched bar, a thinning, a ν ratio. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Lateral strain \varepsilon_{\mathrm{lat}}-0.0003 —Axial strain \varepsilon_{\mathrm{long}}0.001 —

Outputs

Poisson ratio \nu0.300 —

Reading speed

Watch on YouTube

Free library

Full library

Free PDF / open book

YouTube channels

00:0 / 00:08

Narration of this film

A stretched bar, a thinning, a ν ratio.

Poisson's ratio is a thermodynamic elastic constant. For isotropic solids −1 < ν < 0.5, with 0.5 the incompressible limit.

Reading speed

Watch on YouTube