Strain rate

Strain rate, with regards to materials science, is the rate of change in strain with respect to time and is denoted as $\dot {\epsilon}$.

We have

$\dot {\epsilon} = \frac {d \epsilon} {dt} = \frac {d}{dt} \left ( \frac{\ell - \ell_0}{\ell_0} \right ) = \frac{1}{\ell_0} \frac{d\ell}{dt} = \frac{v}{\ell_0}$

where $\ell$ is the length under applied stress, $\ell_0$ is the original length and v is the speed of deformation.

In a Newtonian fluid, the relation between the shear stress and the rate of strain is linear, the constant of proportionality being the coefficient of viscosity.

See also

• Strain
• Strain gauge
• Stress-strain curve
• Stretch ratio