= Strain rate
{title2=$\dot\epsilon$}
{wiki}
<Strain rate> measures how rapidly a material deforms. In a one-dimensional small-<strain> test, $\dot\varepsilon$ 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 tensor>
$$
D=\frac12\left(\nabla\mathbf v+(\nabla\mathbf v)^{\mathsf T}\right).
$$
A 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.
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