# How to Calculate Modulus of Resilience

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"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:

μ = σ12 ÷ 2E

Where σ1 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 × 108 N/m2)2 = 6.25 × 1016 N2/m4

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

2E = 2(2 × 1011 N/m2 ) = 4 × 1011 N/m2

6.25 × 1016 N2/m4 ÷ 4 × 1011 N/m2 = 1.5625 × 105 J/m3

## Tip

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