How to Calculate Modulus of Resilience

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Formulas for Yield Stress
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Updated December 13, 2020
By Kevin Beck

"Resilience" is an engineering term that refers to the amount of energy a material can absorb and still return to its original state. The modulus of resilience μ for a given compound represents the area under the elastic portion of the stress-strain curve for that compound, and is written as:

\mu=\frac{\sigma_1^2}{2E}

Where ​σ​1 is the yield strain and E is Young's modulus.

The modulus of resilience has units of energy per unit volume. In the international system (SI), this is Joules per cubic meter or J/m3. Because a Joule is a Newton-meter, J/m3 is the same as N/m2.

Step 1: Determine the Strain and Young's Modulus

Consult a table of bulk elastic properties of common materials, such as the one on the Georgia State University web page. Using steel as an example, the strain is 2.5 × 108 N/m2 and Young's modulus is 2 × 1011 N/m2.

Step 2: Square The Strain

(2.5 \times 10^8 \text{ N/m}^2)^2 = 6.25 \times 10^{16}\text{ N}^2\text{/m}^4

Step 3: Divide by Twice the Value of Young's Modulus

2E=2(2\times 10^{11}\text{ N/m}^2)=4\times10^{11}\text{ N/m}^2\\\text{ }\\\frac{6.25\times 10^{16}\text{ N}^2\text{/m}^4}{4\times 10^{11}\text{ N/m}^2}=1.5625\times 10^5\text{ J/m}^3

Tip

1 psi (pounds per square inch), another common measure in materials science, is equal to 6.890 J/m3.

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About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.

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