Past exam of the soft condensed matter course of the University of Cambridge / 2012 / Paper 1 / 4 / b / Solution

A relaxation modulus is measured by imposing a step of strain and then holding that strain fixed. Let its amplitude be ${ϵ}_0$, so the initial stress jump is ${\sigma }_0=G_0{ϵ}_0$. For $t>0$, $\dot{ϵ}=0$ and the Maxwell model givesThe 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.