symbols: $M^{\prime\prime}$, $E^{\prime\prime} (\rm{in\ uniaxial\ deformation})$, $G^{\prime\prime} (\rm{in\ simple\ shear\ deformation})$; unit: $\pu{Pa}$
https://doi.org/10.1351/goldbook.12782
Ratio of the amplitude of the stress \(\pu{90\!^{\circ}}\) out of phase with the strain (\(\sigma_{0} \sin \delta\)) to the amplitude of the strain (\(\gamma_{0}\)) in the forced sinusoidal oscillation of a material. \[M^{\prime\prime} = \frac{\sigma_{0} \sin \delta}{\gamma_{0}}\]
Notes:
- For the definitions of the symbols used, see forced sinusoidal oscillation.
- In a linear viscoelastic material, the strain \(\gamma = \gamma_{0} \cos \omega t\) produces a stress \(\sigma = \sigma_{0} \cos (\omega t + \delta) = \sigma_{0} \cos \delta \cos \omega t - \sigma_{0} \sin \delta \sin \omega t\).
- The loss modulus characterises the viscous response of a material.