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Rheologica Acta

Erschienen in:

01.01.2009 | Original Contribution

A new method for the calculation of continuous relaxation spectra from dynamic-mechanical data

verfasst von: Florian J. Stadler, Christian Bailly

Erschienen in: Rheologica Acta | Ausgabe 1/2009

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Abstract

We present a new method for the determination of highly precise continuous relaxation spectra. The method is based on the use of piecewise cubic Hermite splines, which are fairly easy to tabulate by using their knots. The Hermite splines method allows a continuous description of the spectrum by a series of polynomial functions. The numerical instabilities of the spectrum calculation are minimized by limiting the slope of the spectrum to physically meaningful values. The reproducibility of the spectrum calculation is within an error margin of about ±10% in the physically relevant relaxation time range. This method is able to retrieve the spectrum based on data calculated from a benchmark with high accuracy and precision.

Vorheriger Artikel Microstructural investigations of the yielding behaviour of bidisperse magnetorheological fluids

Nächster Artikel A new interpretation for the dynamic behaviour of complex fluids at the sol–gel transition using the fractional calculus

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Or of a retardation time and strength.

Such a low error means that the largest deviation between input and fitted data is in the range of 0.1% (in this case around ω = 10^− 5 s^− 1) and that that deviation is rather the consequence of numerical limitations of double precision numbers than that of a mismatch between the real and the fitted spectrum. Double precision numbers are absolutely required to correctly calculate spectra; otherwise, a very strange result might occur as a consequence of numerical errors.

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Titel: A new method for the calculation of continuous relaxation spectra from dynamic-mechanical data
verfasst von: Florian J. Stadler
Christian Bailly
Publikationsdatum: 01.01.2009
Verlag: Springer-Verlag
Erschienen in: Rheologica Acta / Ausgabe 1/2009
Print ISSN: 0035-4511
Elektronische ISSN: 1435-1528
DOI: https://doi.org/10.1007/s00397-008-0303-2

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