 Strain rate

Strain rate measures how rapidly a material deforms. In a one-dimensional small-strain test, $\dot{\epsilon }$ is extension rate divided by initial gauge length, with units ${\mathrm{s}}^{-1}$. Stretching to the same final strain quickly or slowly can produce different stresses in a rate-dependent material.

For a general flow, the instantaneous local length-change rate is described by the rate-of-strain tensorA material line of current unit direction $\mathbf{n}$ has relative length-change rate $\mathbf{n}\cdot D\mathbf{n}$. This uses the velocity gradient and excludes rigid-body spin. In finite strain theory, $D$ is not simply the componentwise time derivative of every possible finite strain measure. Newtonian fluid stress depends on $D$, while measurements at several strain rates test whether an elastic or plastic model needs explicit rate dependence.

Strain rate is a measure of how quickly a material deforms in response to an applied stress. It quantitatively describes the rate of change of strain with respect to time and is typically expressed in units of inverse time (e.g., s⁻¹).