How to Calculate Modulus of Resilience

••• demarco-media/iStock/Getty Images

"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 ​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 \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.

Related Articles

Formulas for Yield Stress
How to Convert a Load to PSI in a Tensile Test
How to Calculate Ductility
How to Calculate Thermal Stress
Strength of Aluminum Tubing Vs. Steel Tubing
How to Calculate Fastener Pullout
How to Calculate Young's Modulus
How to Calculate Coining Tonnage
Uses of PVC Plastic
What Does HSS Stand for in Steel?
How to Calculate Poisson's Ratio
What Are the Uses of Cobalt?
Properties of Hardened Steel
How to Calculate Section Modulus Pipe
The Mechanical Properties of JIS SCM 420H Steel
HDPE Vs. LDPE
How to Calculate the Mass of a Solid
How to Calculate Rebar Lengths

Dont Go!

We Have More Great Sciencing Articles!