Young's Modulus Calculator

What is Young's Modulus?

Young's modulus, also known as the elastic modulus, is a measure of a solid material's stiffness or resistance to elastic deformation under load. It quantifies the relationship between stress (force per unit area) and strain (proportional deformation) in a material. Young's modulus is a fundamental property in materials science and engineering, crucial for understanding and predicting the behavior of materials under various loading conditions.

Formula

The formula for Young's modulus is:

\[ E = \frac{\sigma}{\varepsilon} \]

Where:

• \( E \) is Young's modulus (typically measured in Pascal, Pa)
• \( \sigma \) (sigma) is the tensile stress (force per unit area)
• \( \varepsilon \) (epsilon) is the extensional strain (proportional deformation)

Calculation Steps

Let's calculate Young's modulus for a material under tension:

1. Given:
   • Stress (\( \sigma \)) = 200 MPa
   • Strain (\( \varepsilon \)) = 0.002 (dimensionless)
2. Apply the Young's modulus formula: \[ E = \frac{\sigma}{\varepsilon} \]
3. Substitute the known values: \[ E = \frac{200 \text{ MPa}}{0.002} \]
4. Perform the calculation: \[ E = 100,000 \text{ MPa} = 100 \text{ GPa} \]

Example and Visual Representation

Let's visualize Young's modulus on a stress-strain curve:

This diagram illustrates:

• The stress-strain curve (blue line) showing the material's behavior under load
• Young's modulus (E) represented by the slope of the red dashed line in the elastic region
• The linear relationship between stress and strain in the elastic region, where Young's modulus is constant
• The x-axis representing strain (ε) and the y-axis representing stress (σ)