Rheologica Acta

, Volume 32, Issue 1, pp 65–73 | Cite as

A nonlinear regularization method for the calculation of relaxation spectra

  • J. Honerkamp
  • J. Weese
Original Contributions

Abstract

It is well known that the relaxation spectrum characterizing the linear viscoelastic properties of a polymer melt or solution is not directly accessible by an experiment. Therefore, it must be calculated from data for a material function. With Tikhonov regularization the relaxation spectrum in the terminal and plateau region can be calculated from data for a material function in the corresponding region. Serious difficulties arise however, if the spectrum should be determined in a larger range. These difficulties are caused by the considerably different contributions at short and long relaxation times. We show that these difficulties can be avoided by a nonlinear regularization method.

Key words

Relaxation spectrum Tikhonov regularization nonlinear regularization 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baumgaertel M, Schausberger A, Winter HH (1990) The relaxation of polymers with linear flexible chains of uniform length. Rheol Acta 29:400–408Google Scholar
  2. Elster C, Honerkamp J (1991) Modified maximum entropy method and its applications to creep data. Macromolecules 24:310 - 314Google Scholar
  3. Elster C, Honerkamp J, Weese J (1992) Using regularization methods for the determination of relaxation and retardation spectra of polymeric liquids. Rheol Acta 31:161–174Google Scholar
  4. Ferry JD (1980) Viscoelastic properties of polymers. J Wiley & Sons, New YorkGoogle Scholar
  5. Friedrich Ch, Hofmann B (1983) Nichtkorrekte Aufgaben in der Rheometrie. Rheol Acta 22:425–434Google Scholar
  6. Groetsch CW (1984) The theory of Tikhonov regularization for Fredholm equations of the first kind. Pitman, LondonGoogle Scholar
  7. Honerkamp J (1989) Ill-posed problems in rheology. Rheol Acta 28:363 - 371Google Scholar
  8. Honerkamp J, Weese J (1989) Determination of the relaxation spectrum by a regularization method. Macromolecules 22:4372 - 4377Google Scholar
  9. Honerkamp J, Weese J (1990) Tikhonovs regularization method for ill-posed problems: A comparison of different methods for the determination of the regularization parameter. Continuum Mech Thermodyn 2:17 - 30Google Scholar
  10. Honerkamp J, Weese J (1993) A note on estimating mastercurves. Rheol Acta 32:57 - 64Google Scholar
  11. Schausberger A, Schindlauer G, Janeschitz-Kriegl H (1985) Linear elasticoviscous properties of molten standard polystyrenes: I. Presentation of complex moduli; role of short range structural parameters. Rheol Acta 24:220 - 227Google Scholar
  12. Weese J (1992) A reliable and fast method for the solution of Fredholm integral equations of the first kind based on Tikhonov regularization. Comput Phys Commun 69:99–111Google Scholar
  13. Weese J (in preparation) A regularization method for nonlinear ill-posed problemsGoogle Scholar
  14. Wiff DR, Gehatia M (1975) Inferring mechanical relaxation spectra as an ill-posed problem. J Appl Phys 46 (10):4231–4234Google Scholar
  15. Wiff DR (1978) RQP method of inferring a mechanical relaxation spectrum. J Rheol 22 (6):589 - 597Google Scholar

Copyright information

© Steinkopff-Verlag 1993

Authors and Affiliations

  • J. Honerkamp
    • 1
    • 2
  • J. Weese
    • 1
  1. 1.University of FreiburgGermany
  2. 2.Fakultät für PhysikUniversität FreiburgFreiburg i. Br.Germany

Personalised recommendations