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Young's Modulus
Young's modulus (E) is a measure of the stiffness of a material, describing its resistance to elastic deformation when a force is applied.
It is defined as the ratio of stress (force per unit area) to strain (proportional deformation) in the elastic region of a material.
More Information
What is Young's Modulus?
Young's modulus, also known as the elastic modulus or modulus of elasticity, is a mechanical property that measures a material's stiffness or resistance to elastic deformation under load. It is named after the British scientist Thomas Young.
Young's modulus is defined as the ratio of stress (force per unit area) to strain (proportional deformation) in the linear elastic region of a material. Mathematically, it is expressed as:
Where:
E = Young's modulus
σ (sigma) = Stress
ε (epsilon) = Strain
Stress-Strain Diagram
The graph above illustrates the relationship between stress and strain. Young's modulus (E) is represented by the slope of the straight line in the elastic region. The steeper the slope, the stiffer the material.
Stress
Stress is the force applied per unit area:
Where:
- F = Applied force
- A = Cross-sectional area
Units: Pa, MPa, GPa, psi, ksi
Strain
Strain is the relative deformation of a material:
Where:
- ΔL = Change in length
- L = Original length
Units: Dimensionless (often expressed as mm/mm or in/in)
Deformation
Deformation can be calculated using:
Where:
- δ = Deformation
- F = Applied force
- L = Original length
- E = Young's modulus
- A = Cross-sectional area
Materials Comparison
Young's modulus values for common materials:
| Material | E (GPa) |
|---|---|
| Steel | 200 |
| Aluminum | 69 |
| Copper | 117 |
| Concrete | 30 |
| Glass | 70 |
| Oak (along grain) | 11 |
Applications
Young's modulus is used in:
- Structural design calculations
- Material selection for specific applications
- Finite element analysis (FEA)
- Beam deflection calculations
- Vibration analysis
- Elastic stability calculations
Limitations
Important considerations:
- Only valid in the linear elastic region
- Values vary with temperature
- Anisotropic materials have different values in different directions
- Not applicable in plastic deformation
- Material properties may vary from sample to sample
Hooke's Law and Young's Modulus
Young's modulus is closely related to Hooke's Law, which states that the force needed to extend or compress a spring is proportional to the distance it is stretched. In terms of stress and strain, Hooke's Law is expressed as:
This linear relationship holds true only up to a point called the elastic limit. Beyond this limit, materials enter the plastic deformation region where the relationship is no longer linear and permanent deformation occurs.