Young Modulus

The value of a Stiffness Constant only applies to a certain sample. F_or example, a longer piece of the same material would have a lower stiffness constant._ The Young Modulus on the other hand is a material property, meaning it can be applied to all samples of the same material. It is calculated by the formula:

$Young,Modulus=\frac{Stress}{Strain}$ $E=\frac{\sigma}{\varepsilon}$

Stress and Strain

Stress is a measure of the force applied per unit cross-sectional area of a material. It is measured in Pascals (Pa, or Nm^-2, or Kgm^-1s^-2 if you want to be pedantic). It is hence calculated by the formula:

$Stress,:\sigma=\frac{force}{cross-sectional;;area}$

Strain is the change in length relative to original length. It has no units since it is the ratio of two lengths. It is calculated by the formula:

$Strain,:\vare=\frac{extension}{original;;length}$

A stress on a material causes a strain.

For a material, a stress-strain graph can be drawn. The gradient of this graph is then the Young Modulus. The Young Modulus is also measured in Pascals. By finding the area under a stress-strain graph, it is possible to work out the energy stored per unit volume in a material.

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The Young Modulus, being a material property as it is, can be used to generalise the elastic properties of a material. This is very useful, for example, in working with seat belts, as it important to be able to calculate how far they will stretch for any length or thickness.