COMPUTATION OF THE LINEAR VISCOELASTIC RELAXATION SPECTRUM FROM EXPERIMENTAL-DATA

Accurate and reliable determination of the linear viscoelastic relaxat ion spectrum is a critical step in the application of any constitutive equation. The experimental data used to determine the relaxation spec trum always include noise and are over a limited time or frequency ran ge, both of which can affect the determination of the spectrum. Regula rization with quadratic programming has been used to derive the spectr um; however, because both the experimental data and the spectrum chang e by more than an order of magnitude, the input data and the spectrum are normalized in order for the numerical procedure to be accurate. Ac curate determination of the relaxation spectrum requires that the spec trum extend about two logarithmic decades on either side of the freque ncy range of the input data. The spectrum calculated from G '' alone i s more accurate at shorter relaxation times, while that from G' data a lone is more accurate at longer relaxation times. Therefore, for best results, the spectrum is obtained from a combination of G' and G '' da ta, blended in the manner described herein. Comparison with existing m ethods 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.