A cube of side 0.20 m is compressed by a uniaxial stress of 300 MPa. The side length decreases by 0.30 mm along the load direction and increases by 0.15 mm perpendicular to the load. What is the Poisson’s ratio of the material?

Step-by-step solution

1. Compute axial strain: ${ϵ}_{ax}=\frac{\Delta L_{ax}}{L_0}=\frac{-0.30\text{mm}}{200\text{mm}}=-0.0015$.
2. Compute lateral strain: ${ϵ}_{lat}=\frac{\Delta L_{lat}}{L_0}=\frac{+0.15\text{mm}}{200\text{mm}}=0.00075$.
3. Use definition of Poisson’s ratio: $\nu =-\frac{{ϵ}_{lat}}{{ϵ}_{ax}}$.
4. Substitute the strains: $\nu =-\frac{0.00075}{-0.0015}=0.5$.
5. Thus the Poisson’s ratio is 0.5.

Concept tested: Poisson’s ratio calculation

Published 10 October 2026 · How this solution was prepared and checked