Young's Modulus (Elastic Modulus)
Reference for Young's Modulus E = stress / strain.
The fundamental material property describing how much a solid stretches under tension or compression.
Definition
Young's Modulus E is the constant of proportionality between stress and strain in the linear elastic region of a material. It is a measure of how much a solid object stretches or compresses under an applied load.
A high Young's Modulus means the material is stiff — large stress produces small strain. A low Young's Modulus means the material is flexible — small stress produces noticeable strain.
Variables
| Symbol | Meaning | Typical Unit |
|---|---|---|
| E | Young's Modulus | Pa (often GPa) |
| σ (sigma) | Stress = Force per area | Pa or N/m² |
| ε (epsilon) | Strain = ΔL / L₀ (dimensionless ratio) | unitless |
| F | Applied force | N |
| A | Cross-sectional area | m² |
| L₀ | Original length | m |
| ΔL | Change in length | m |
Typical Values
| Material | Young's Modulus (GPa) |
|---|---|
| Diamond | ~1100 |
| Tungsten carbide | ~530 |
| Steel (structural) | ~200 |
| Titanium | ~116 |
| Brass | ~100 |
| Aluminum | ~69 |
| Glass | ~50-90 |
| Concrete | ~30 |
| Wood (along grain) | ~10-15 |
| Bone (cortical) | ~14 |
| Polyethylene | ~0.8 |
| Rubber | ~0.01-0.1 |
Example — Steel Wire
A 2 m steel wire of cross-section 4 mm² stretches 0.5 mm when pulled with 800 N. Find Young's Modulus.
A = 4 mm² = 4 × 10⁻⁶ m²
σ = F / A = 800 / (4 × 10⁻⁶) = 2 × 10⁸ Pa = 200 MPa
ε = ΔL / L₀ = 0.0005 / 2 = 2.5 × 10⁻⁴
E = σ / ε = 2 × 10⁸ / 2.5 × 10⁻⁴
E = 8 × 10¹¹ Pa = 800 GPa
Note: real structural steel is closer to E ≈ 200 GPa. The example uses idealized numbers.
When the Formula Applies
The simple linear relationship E = σ / ε is only valid in the elastic region — small strains where the material returns to its original shape when the load is removed. Beyond the yield point, the material deforms plastically and Young's Modulus no longer describes the response.
For most metals, the elastic region runs to strains of about 0.001 to 0.003 before yielding. Polymers and biological tissues often have non-linear stress-strain curves even at small strains and require more complex models.
When to Use It
- Sizing structural members for deflection limits
- Designing springs and elastic mechanical elements
- Predicting natural frequencies of beams and plates
- Computing thermal stress when constrained materials are heated
- Comparing material stiffness for selection decisions