 Solution

Use a rheometer, for example a cone-and-plate rheometer or a parallel-plate rheometer, to impose a small deformation and measure the required torque, or impose a torque and measure the deformation. The apparatus geometry converts these into shear stress and strain. First check that reducing the imposed amplitude does not change the normalized response; this identifies the linear regime and avoids yielding or structural rearrangement.

Three complementary protocols characterize the material's memory. In a stress relaxation experiment impose a small step ${ϵ}_{0}H(t)$ and hold the deformation fixed. The output is the relaxation modulus $G(t)=\sigma (t)/{ϵ}_0$, revealing how stored stress decays and whether an elastic plateau remains. In a creep compliance measurement impose a small stress step ${\sigma }_{0}H(t)$ and record $J(t)=ϵ(t)/{\sigma }_0$. Removing the load also distinguishes recoverable deformation from permanent flow.

In small-amplitude oscillatory shear, impose sinusoidal strain over a range of frequencies and measure both stress amplitude and phase. With $ϵ={ϵ}_0\cos \omega t$, fitThe outputs are the storage modulus $G^{\prime }$ and loss modulus $G^{\prime \prime }$, or equivalently amplitude ratio and loss tangent $\tan \delta =G^{\prime \prime }/G^{\prime }$. These measure elastic storage and dissipative response, respectively. The step experiments give time-domain information and the oscillatory experiment gives the corresponding frequency-domain response. All comparisons must use the same deformation convention and controlled temperature.