A sign control method for fitting and interconverting material functions for linearly viscoelastic solids

R. D. Bradshaw*, L. C. Brinson

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

73 Scopus citations


The multidata method was originally proposed to fit a Prony exponential series function to experimental viscoelastic modulus and compliance data; this was accomplished by the application of a linear least squares solver. This paper considers a similar approach, but extended in two key ways. First, it has been applied to the solution of convolution integral equations; specifically those used for material function interconversion. Second, it has been modified to force the signs of the Prony series coefficients to be positive; this is an essential criterion for the proper physical interpretation of a Prony series material function, which is typically not satisfied by multidata method solutions. Sign control is implemented by an iterative Levenberg-Marquardt solution algorithm with an appropriate constraint, and can be used for both fitting experimental data and interconversion. To use the method, a Prony series must be capable of adequately representing the applicable functions. The method is demonstrated by first fitting and converting experimental modulus data. Formulation for a composite lamina is also shown, in which a system of integral equations is reduced to a single integral equation; this can then be solved using the new method. Finally, application of the new method to frequency domain transformations is demonstrated, along with comparisons to other techniques.

Original languageEnglish (US)
Pages (from-to)85-108
Number of pages24
JournalMechanics of Time-Dependent Materials
Issue number1
StatePublished - Jan 1 1997


  • Composites
  • Interconversion
  • Linear viscoelasticity
  • Material functions
  • Multidata method
  • Prony series
  • Spectrum methods

ASJC Scopus subject areas

  • Chemical Engineering(all)
  • Materials Science(all)
  • Aerospace Engineering
  • Mechanical Engineering

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