= Solution
A <relaxation modulus> is measured by imposing a step of <strain> and then holding that <strain> fixed. Let its amplitude be $\epsilon_0$, so the initial <stress> jump is $\sigma_0=G_0\epsilon_0$. For $t>0$, $\dot\epsilon=0$ and the <Maxwell model> gives
$$
\dot\sigma=-\frac{G_0}{\eta}\sigma,
\qquad\sigma(t)=\sigma_0e^{-t/\tau},\qquad
\boxed{G(t)=\frac{\sigma(t)}{\epsilon_0}=G_0e^{-t/\tau},\quad\tau=\eta/G_0.}
$$
The initial <stress> in the wording must be understood as that produced by the initial deformation. If an external apparatus instead maintains $\sigma=\sigma_0$, the <stress> does not decay: the experiment is creep, considered below. Merely specifying an initial <stress> without a subsequent constraint would not uniquely prescribe the relaxation experiment.
Back to article page
