Important Inequalities Among Viscoelastic Functions

Some important inequalities among viscoelastic functions can be developed by analyzing their mathematical expressions. For example, the difference between G ((o) and G t = l/m) can be written as (1,2) 

5 DETEHMINATION OF VISCOSITY AND STEADY-STATE (EQUILIBRIUM) COMPLIANCE FROM RELAXATION AND RETARDATION SPECTRA 

Methods have been described in preceding sections to relate and r to viscoelastic functions in limit conditions, for example, when o) - 0. In this section, the procedures to evaluate these parameters from the relaxation and retardation spectra are analyzed. 

Both the steady-state compliance function, and the equilibrium compliance, Jg, can readily be obtained from the retardation spectrum. Actually, by taking the limit of Eq. (9.20) in the limit oo 0, the following relationship for Jg and Jg is obtained  

This equation also allows us to determine the mean relaxation time from q and /g. Actually, the mean relaxation time, (t), can be expressed as 

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