Dissipated energy per oscillatory shear cycle ($W_{\mathrm{cycle}}/V=\pi G^{\prime \prime }{\gamma }_0^2$)

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.