Re-examination of the approximate methods for interconversion between frequency- and time-dependent material functions

The paper examines the correctness of the best-known approximate methods of interconversion between the frequency- and the time-dependent material functions. Approximate interconversions are compared to the close-form viscoelastic interrelations through the relaxation and/or retardation spectra. The analysis showed that the simple method, G(t) ≃G′(ω)|ω=1/t, should be avoided. The most successful was the method of Schwarzl yielding results with maximum relative error within 2%. The magnitude of the error of interconversion is related to the magnitude of the response function first derivative. When the first derivative ψ = |d(log G′(ω))/d(log(ω))| < 0.5 all approximate methods except the simple method furnish interconversions within the acceptable error, i.e., less than 5%.