How To Calculate Modulus Of Resilience

"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.