Prediction of the Shift Factors for Viscoelastic Solids

When CO 0, the loss compliance function for viscoelastic solids is given by 

This equation suggests a procedure to obtain the real component of the complex viscosity from the compliance functions at zero frequency. By taking Eq. (8.29) into account, Eq. (8.27) can be rewritten as 

By applying the time-temperature correspondence principle to / (co) and / (co) at low frequencies, one obtains 

These equations lead to the following expression for the shift factor (3)  

This expression is similar to the one obtained for viscoelastic liquids [Eq. (8.25)], the only difference being that r is the zero shear rate viscosity in liquids while q (0) for viscoelastic solids represents the real component of the complex viscosity at zero frequency. 

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