Poisson’s ratio is a fundamental mechanical property of materials that describes the ratio of transverse strain to axial strain when a material is subjected to uniaxial stress. Named after the French mathematician Siméon Denis Poisson, it plays a crucial role in understanding material deformation under various loading conditions.
When a material is stretched or compressed along one axis, it tends to expand or contract along the perpendicular directions. Mathematically, Poisson’s ratio (ν) is expressed as:
ν = - (Transverse Strain / Axial Strain) = - (Δd/d) / (ΔL/L)
Where:
The negative sign accounts for the fact that an increase in axial length usually results in a decrease in lateral dimensions and vice versa.
Poisson’s ratio varies between materials:
Poisson’s ratio is intrinsically linked to other elastic properties of materials, including the Shear Modulus (G) and Bulk Modulus (K) where E is Young's Modulus.
G = E / [2(1 + ν)]
Where E is the Young's Modulus.
K = E / [3(1 - 2ν)]
These relationships illustrate how Poisson’s ratio connects the deformation characteristics of a material under shear and volumetric stress.
| Material | Poisson’s Ratio (ν) |
|---|---|
| Rubber | 0.49 – 0.50 |
| Steel | 0.27 – 0.30 |
| Concrete | 0.20 – 0.25 |
| Glass | 0.18 – 0.30 |
| Aluminum | 0.33 |
| Copper | 0.33 |
| Titanium | 0.30 |
| Cork | ~0.0 |
| Auxetic Materials | Negative (-0.1 to -0.8) |
Auxetic materials, characterized by their negative Poisson’s ratios, are an exciting area of research. These materials expand perpendicular to applied tension, offering unique properties like enhanced energy absorption and fracture resistance.
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