How to Calculate Modulus of Resilience

By Samuel Markings; Updated April 24, 2017
The modulus of resilience varies from material to material.

All bulk materials can be characterized in terms of their elasticity. Some materials, such as rubber have a high elasticity, whereas others such as wood have much lower values. The modulus of resilience is a quantity that describes the maximum amount of energy a material absorbs when a load (force) is applied.

Determine the material for which you require the modulus of resilience. The following properties will be required for this material:

You will need to know Young's modulus, which quantifies the amount a material stretches when a given force is applied, along with yield strength -- the stress that is required to produce elastic deformation within a material.

For the sake of this example, lets use aluminium material:

Yield strength = 93 x 10^6 Newton's per square meter

Young's modulus = 69 x 10^9 Newton's per square meter

Write down the equation for modulus of resilience:

Modulus of resilience = (Yield strength)^2 / ( 2 x Young's Modulus)

Plug the numbers into the equation. Following the example for aluminium, the modulus of resilience is:

Modulus of resilience = (93 x 10^6)^2 / (2 x 69 x 10^9) = 62673.9 Newtons per square meter (8.7 psi).

About the Author

Samuel Markings has been writing for scientific publications for more than 10 years, and has published articles in journals such as "Nature." He is an expert in solid-state physics, and during the day is a researcher at a Russell Group U.K. university.