Past exam of the materials science course of the University of Cambridge / 2018 / Paper 1 / 6 / b / Solution

Interpret the supplied real quantity as the storage modulus $E^{\prime }$, with $k$ the spring modulus in this continuum representation and $\eta$ the corresponding viscosity. Let $\tau =t_R=\eta /k$. ThenAt high frequency, $\omega \tau \gg 1$, the response approaches the spring stiffness; at low frequency it becomes much softer:In the series Maxwell model, the spring and dashpot carry the same stress while their strains add. A rapidly changing load allows little viscous flow, so the spring dominates the strain response. Over a long cycle the dashpot has time to deform, giving a small storage modulus and a fluid-like low-frequency response. This is generic viscoelastic mechanics, independent of the biological parts deferred above.