symbols: $M^{\prime}$, $E^{\prime} (\rm{in\ uniaxial\ deformation})$, $G^{\prime} (\rm{in\ simple\ shear\ deformation})$; unit: $\pu{Pa}$
https://doi.org/10.1351/goldbook.12802
Ratio of the amplitude of the stress in phase with the strain (\(\sigma_{0} \cos \delta\)) to the amplitude of the strain (\(\gamma_{0}\)) in the forced sinusoidal oscillation of a material. \[M^{\prime} = \frac{\sigma_{0} \cos \delta}{\gamma_{0}}\]
Notes:
- Definition taken, with "forced sinusoidal oscillation" replacing "forced oscillation".
- 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 storage modulus characterises the elastic response of a material.