Maxwell dissipation under controlled stress and strain

For a series Maxwell model with $\tau =\eta /k$, $E^{\prime \prime }=k\omega \tau /(1+{\omega }^2{\tau }^2)$. At fixed strain amplitude the energy dissipated per cycle is $\pi E^{\prime \prime }{\epsilon }_0^2$ and peaks at $\omega \tau =1$. At fixed stress amplitude it is instead $\pi {\sigma }_0^2/(\eta \omega )$, which has no finite-frequency maximum. Specifying the imposed variable and whether loss means energy per cycle or power is essential.