Loss modulus ($G^{\prime \prime }$)

The loss modulus is the quadrature coefficient $G^{\prime \prime }$ in oscillatory shear. It measures viscous energy dissipation.

For strain $\gamma ={\gamma }_0\cos \omega t$ and stress $\sigma ={\gamma }_0(G^{\prime }\cos \omega t-G^{\prime \prime }\sin \omega t)$, integrating supplied power $\sigma \dot{\gamma }$ over one period gives the displayed dissipated energy per unit volume. The storage term integrates to zero; passivity requires nonnegative loss modulus for positive frequency in this convention.