Rheologica Acta

, Volume 32, Issue 6, pp 589–600

The extended Padé-Laplace method for efficient discretization of linear viscoelastic spectra

  • M. Simhambhatla
  • A. I. Leonov

DOI: 10.1007/BF00369076

Cite this article as:
Simhambhatla, M. & Leonov, A.I. Rheol Acta (1993) 32: 589. doi:10.1007/BF00369076


The discretization of linear viscoelastic spectra is valuable as a starting point for non-linear viscoelastic modeling. However, obtaining the parameters of the generalized Maxwell model from linear viscoelastic experiments with naive least squares procedures is known to be an ill-posed problem. A novel technique, the Padé-Laplace method was recently elucidated (Fulchiron et al., 1993) for robustly extracting the parameters of the generalized Maxwell model from stress relaxation experiments, without any a priori assumption about the number of Maxwellian modes. We extend this method for obtaining the Maxwellian modes from dynamic data and discuss the relationship between continuous viscoelastic spectra and the Maxwellian modes obtained by this procedure. Furthermore, the applicability of this method with experimental data in limited time/frequency windows is clarified. Finally, a procedure for assembling the discretized spectrum with the Padé-Laplace method applied to both stress relaxation and dynamic data with typical experimental time/frequency cutoffs is developed.

Key words

Maxwell modelviscoelasticityLaplace transformPadé-Laplace method

Copyright information

© Steinkopff-Verlag 1993

Authors and Affiliations

  • M. Simhambhatla
    • 1
  • A. I. Leonov
    • 1
  1. 1.Dept. of Polymer EngineeringThe University of AkronAkronUSA