Modulus of Resilience Calculator

What is Modulus of Resilience?

The Modulus of Resilience (U_r) is the maximum energy per unit volume that a material can absorb and still return to its original shape when the load is removed. It represents the material's ability to absorb energy without permanent deformation.

How to Use This Calculator

1. Enter the Yield Strength of your material in MPa. This is the stress at which a material begins to deform plastically.
2. Enter the Poisson's Ratio of your material. This is a dimensionless quantity that measures the ratio of transverse strain to longitudinal strain in a material.
3. Click the Calculate button to compute the Modulus of Resilience.
4. The result will be displayed in MPa.

Working Principle

The Modulus of Resilience is calculated using the formula:

U_r = (σ_y²)/(2(1+ν))

This formula derives from the elastic energy stored in a material under uniaxial stress, considering both the stress at yield and the material's Poisson's ratio.

Applications

The Modulus of Resilience is an important property in material science and engineering, used in:

• Designing components that need to absorb impact energy (e.g., bumpers, shock absorbers)
• Assessing material suitability for cyclic loading applications
• Comparing material properties for specific engineering applications

Example

If a material has a yield strength of 300 MPa and a Poisson's ratio of 0.3, its modulus of resilience would be:

U_r = (300²)/(2(1+0.3)) = 30000/2.6 ≈ 11538.46 MPa