Poisson's Ratio

Poisson's Ratio

Poisson's ratio is the ratio of lateral strain to longitudinal strain.

### Formula

$$\sigma=-\frac{Lateral\ Strain}{Longitudinal\ Strain}$$

### Expanded Form

$$\sigma=-\frac{\Delta d/d}{\Delta L/L}$$

### Terminologies

- σ → Poisson's ratio.

- Δd → Change in lateral dimension.

- d → Original lateral dimension.

- ΔL → Change in length.

- L → Original length.

### SI Unit

No unit

### Dimensions

$$[\sigma]=[M^0L^0T^0]$$

### Conditions / Special Cases

For most materials:

$$0<\sigma<0.5$$

Maximum value:

$$\sigma=\frac{1}{2}$$

### Usage

- Used in elasticity and material deformation problems.