# Young's modulus

## Definition

Young's modulus is defined as the ratio of the uniaxial stress over the uniaxial strain in the range of stress in which Hooke's Law holds.

## Unit

Young's modulus has the unit of pressure which is $N/m^2$.

## Usage

The Young's modulus allows the behavior of a bar made of an isotropic elastic material to be calculated under tensile or compressive loads. For instance, it can be used to predict the amount a wire will extend under tension or buckle under compression. Some calculations also require the use of other material properties, such as the shear modulus, density, or Poisson ratio.

## Expression

Young's modulus, Y, can be calculated by dividing the tensile stress by the tensile strain:

$Y \equiv \frac{\mbox {tensile stress}}{\mbox {tensile strain}} = \frac{\sigma}{\varepsilon}= \frac{F/A_0}{\Delta L/L_0} = \frac{F L_0} {A_0 \Delta L}$

where

Y is the Young's modulus (modulus of elasticity)
F is the force applied to the object;
A0 is the original cross-sectional area through which the force is applied;
ΔL is the amount by which the length of the object changes;
L0 is the original length of the object.