Past exam of the soft condensed matter course of the University of Cambridge / 2021 / Section B / 4 / c

Parallel elements have the same strain, while their stresses add. The spring supplies $G_0ϵ$ and the viscous element supplies ${\eta }_0\dot{ϵ}$, so the Kelvin-Voigt model has constitutive equationFor the oscillatory deformation this givesPhysical stress and strain are the real parts of these expressions. Thus the storage modulus is $G_0$, independent of frequency, and the loss modulus is $\omega {\eta }_0$. The equation is the quasistatic material law; an inertial equation for an attached mass would require additional mechanical data.