"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 = *σ*_{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/m^{3}. Because a Joule is a Newton-meter, J/m^{3} is the same as N/m^{2}.

## 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 × 10^{8} N/m^{2} and Young's modulus is 2 × 10^{11} N/m^{2}.

## Step 2: Square The Strain

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

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

2E = 2(2 × 10^{11} N/m^{2} ) = 4 × 10^{11} N/m^{2}

6.25 × 10^{16} N^{2}/m^{4} ÷ 4 × 10^{11} N/m^{2} = 1.5625 × 10^{5} J/m^{3}

## Tip

1 psi (pounds per square inch), another common measure in materials science, is equal to 6.890 J/m^{3}.

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