Young Modulus

Measure of elasticity of a material

E=σϵ=FlxAYoung modulus=stressstrain=normal force⋅original lengthextension⋅cross-sectional area\begin{align*} E &= \frac{\sigma}{\epsilon} \\ &= \frac{Fl}{xA} \\ \text{Young modulus} &= \frac{\text{stress}}{\text{strain}} \\ &= \frac{\text{normal force} \cdot \text{original length}}{\text{extension} \cdot \text{cross-sectional area}} \end{align*}

Unit of EE = Pa\mathrm{Pa}

Note: Young Modulus is typically measured in MPa\mathrm{MPa} or GPa\mathrm{GPa}

Stress (σ\sigma)

Normal force applied per unit cross-sectional area
(same as the definition of pressure!)

σ=FAstress=normal forcecross-sectional area\begin{align*} \sigma &= \frac{F}{A} \\ \text{stress} &= \frac{\text{normal force}}{\text{cross-sectional area}} \end{align*}

Unit of σ\sigma = Pa\mathrm{Pa}

Strain (ϵ\epsilon)

Ratio of change in length

ϵ=xlstrain=extensionoriginal length\begin{align*} \epsilon &= \frac{x}{l} \\ \text{strain} &= \frac{\text{extension}}{\text{original length}} \end{align*}

Unit of ϵ\epsilon = no unit