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Calculating 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.

Tip

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

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