Computation of the linear viscoelastic relaxation spectrum from experimental data

Accurate and reliable determination of the linear viscoelastic relaxation spectrum is a critical step in the application of any constitutive equation. The experimental data used to determine the relaxation spectrum always include noise and are over a limited time or frequency range, both of which can affect the determination of the spectrum. Regularization with quadratic programming has been used to derive the spectrum; however, because both the experimental data and the spectrum change by more than an order of magnitude, the input data and the spectrum are normalized in order for the numerical procedure to be accurate. Accurate determination of the relaxation spectrum requires that the spectrum extend about two logarithmic decades on either side of the frequency range of the input data. The spectrum calculated from G '' alone is more accurate at shorter relaxation times, while that from G' data alone is more accurate at longer relaxation times. Therefore, for best results, the spectrum is obtained from a combination of G' and G '' data, blended in the manner described herein. Comparison with existing methods in the literature shows a consistently improved performance of the present method illustrated with both model as well as experimental data. (C) 1997 John Wiley & Sons, Inc.