Houjun Liu

Elastic Modulus

The Elastic Modulus is a measurement of how much deformation takes place given some force on the system. Formally, it is the slope of the stress-strain curve, defined by:

\begin{equation} E = \frac{stress}{strain} \end{equation}

The units in pascals as it is: force per area (pascals) divided by deformation (dimensionless, as it is a fraction of old shape over new shape \(\frac{V}{V}=1\)).

Depending on how its measured, it is called different things:

  • Young’s Modulus: tensile elasticity—tendency for object to deform along an axis with force applied (usually that is just called the Elastic Modulus)
  • Shear’s Modulus: shear elasticity—tendency of an object to shear (deform in shape with the constant volume) with force applied
  • Bulk Modulus: volumetric elasticity—tendency for an object to deform in all directions when uniformly loaded