Table of Contents
What Is Poisson's Ratio?
Poisson's ratio (ν) measures the Poisson effect, the tendency of a material to expand perpendicular to compression or contract perpendicular to stretching. When you pull a rubber band, it gets thinner in the middle. When you compress clay, it bulges outward. Poisson's ratio quantifies this cross-sectional response relative to the applied deformation.
For most materials, Poisson's ratio ranges from 0 to 0.5. A value of 0.5 represents a perfectly incompressible material where volume is conserved during deformation. Cork has a ratio near zero, which is why it works as a bottle stopper without expanding laterally. Some auxetic metamaterials have negative values, expanding laterally when stretched, and find use in impact-resistant armor and biomedical implants.
Formulas and Relations
These relationships connect all four elastic constants for isotropic materials. Any two are sufficient to derive the others. G is the shear modulus (resistance to shape change), K is the bulk modulus (resistance to volume change), and λ is Lame's first parameter used in stress-strain tensors.
Typical Poisson's Ratio Values
| Material | Poisson's Ratio | Young's Modulus (GPa) |
|---|---|---|
| Steel | 0.27 - 0.30 | 200 |
| Aluminum | 0.33 | 69 |
| Copper | 0.34 | 117 |
| Rubber | 0.499 | 0.01 - 0.1 |
| Cork | ~0 | 0.013 |
| Concrete | 0.1 - 0.2 | 30 |
| Glass | 0.18 - 0.30 | 50 - 90 |
Frequently Asked Questions
Can Poisson's ratio be negative?
Yes. Materials with negative Poisson's ratio are called auxetic materials. They expand laterally when stretched. Examples include re-entrant foams, certain crystals, and engineered metamaterials. These find applications in blast-resistant structures and medical stents that expand when pulled.
Why is 0.5 the upper theoretical limit?
A ratio of 0.5 means the material is perfectly incompressible with zero volume change under deformation. Values above 0.5 would imply the material gains volume when compressed, violating thermodynamic stability for isotropic materials. The bulk modulus would become negative, which is physically impossible for stable materials.
How is Poisson's ratio measured?
It is measured by applying a uniaxial load and simultaneously measuring axial and lateral strain with strain gauges or extensometers. Modern digital image correlation (DIC) techniques can map the full strain field non-contactly, providing Poisson's ratio across the entire specimen surface.