Young's Modulus

Young's Modulus (Y)

A measure of the stiffness of an elastic material, equal to the ratio of the longitudinal stress to the longitudinal strain within the elastic limit.

Longitudinal Stress

The force applied per unit cross-sectional area that tends to stretch or compress an object along its length.

Longitudinal Strain

The fractional change in length of an object when subjected to longitudinal stress; defined as the change in length divided by the original length.

Elastic Limit

The maximum stress that a material can withstand without permanent deformation. Beyond this limit, the material may not return to its original shape after the stress is removed.

Young's Modulus

Where σ is longitudinal stress and ε is longitudinal strain.

Y = \frac{\σ}{\varepsilon}

Longitudinal Stress

F is the applied force perpendicular to the cross-sectional area A.

\σ = \frac{F}{A}

Longitudinal Strain

ΔL is the change in length and L₀ is the original length.

\varepsilon = \frac{\Δ L}{L₀}

Young's Modulus (Combined)

This combines the definitions of stress and strain into the Young's modulus formula.

Y = \frac{F/A}{\Δ L/L₀} = \frac{F L₀}{A \Δ L}