Poisson's Ratio Converter - Calculate Material Properties & Elastic Constants
Calculated Poisson's Ratio:
ν = -0.001 / 0.003 = -0.3333
Reference: Steel has ν = 0.27
How Poisson's Ratio Works
Apply Load
Material under axial stress
Measure Strains
Axial and lateral deformation
Calculate Ratio
Apply Poisson's formula
Formulas and Calculations
Basic Formula
ν = -εₗ/εₐ
Where:
- ν = Poisson's ratio
- εₗ = Lateral strain
- εₐ = Axial strain
Relationship with Elastic Moduli
ν = (E/2G) - 1
Where:
- E = Young's modulus
- G = Shear modulus
Bulk Modulus Relation
K = E/[3(1-2ν)]
Where:
- K = Bulk modulus
- E = Young's modulus
Volume Change
ΔV/V = εₐ(1-2ν)
Where:
- ΔV/V = Volumetric strain
- εₐ = Axial strain
Material Properties Table
| Material | Poisson's Ratio (ν) | Category | Typical Range |
|---|---|---|---|
| Steel | 0.27 | Metal | 0.10-0.30 |
| Aluminum | 0.33 | Metal | 0.30-0.40 |
| Copper | 0.34 | Metal | 0.30-0.40 |
| Concrete | 0.20 | Composite | 0.10-0.30 |
| Glass | 0.22 | Ceramic | 0.10-0.30 |
| Rubber | 0.50 | Polymer | 0.40-0.50 |
| Cork | 0.00 | Natural | 0.00-0.10 |
| Titanium | 0.32 | Metal | 0.30-0.40 |
| Brass | 0.35 | Metal | 0.30-0.40 |
| Wood (Oak) | 0.40 | Natural | 0.40-0.50 |
| Plastic (PVC) | 0.38 | Polymer | 0.30-0.40 |
| Carbon Fiber | 0.25 | Composite | 0.10-0.30 |
| Granite | 0.25 | Natural | 0.10-0.30 |
| Lead | 0.44 | Metal | 0.40-0.50 |
| Nickel | 0.31 | Metal | 0.30-0.40 |
Material Categories Chart
Metal
Polymer
Ceramic
Natural
Practice Problems
Problem 1:
Steel rod: εₐ = 0.002, εₗ = -0.00054. Find ν.
Solution: ν = -(-0.00054)/0.002 = 0.27
Problem 2:
Aluminum: E = 70 GPa, G = 26 GPa. Find ν.
Solution: ν = (70/2×26) - 1 = 0.35
Problem 3:
Concrete: ν = 0.2, εₐ = 0.001. Find εₗ.
Solution: εₗ = -ν × εₐ = -0.2 × 0.001 = -0.0002
Problem 4:
Rubber: ν = 0.5, find volume change under tension.
Solution: ΔV/V = εₐ(1-2×0.5) = 0 (incompressible)
Problem 5:
Glass: ν = 0.22, E = 70 GPa. Find bulk modulus K.
Solution: K = 70/[3(1-2×0.22)] = 41.7 GPa
Daily Uses of Poisson's Ratio
Bridge design requires accurate material deformation predictions
Medical implants use biocompatible materials with specific ratios
Automotive parts design considers stress distribution patterns
Building foundations analyze soil and concrete behavior
Aerospace components require precise material property calculations