Prony series and spectral function characterization of viscoelastic compliances of a solid polymer

  • Jutima Simsiriwong Auburn University
  • Rani Warsi Sullivan Mississippi State University
  • Harry H Hilton


This paper presents two characterization methods that are used to describe viscoelastic behavior.  In the Prony series method, a discrete representation of the generalized Kelvin model is used, whereas the spectral method uses a continuous distribution. The Prony series coefficients are determined through the linear least squares technique. The Elastic-Viscoelastic Correspondence Principle and the Laplace transform are used in the spectral function approach, which utilizes a selected distribution function that has the potential to describe a wide range of viscoelastic material behavior. Characterization exercises from both methods used strain histories from short-term unidirectional tensile creep experiments that were obtained at three temperatures below the glass transition temperature of a vinyl ester polymer. Experimental strains in both the longitudinal and transverse directions were measured using the digital image correlation technique and linear viscoelastic material properties were obtained without using Poisson’s ratios. The measured data was subsequently used to determine the tensile creep compliance function for each test configuration. The potential and limitations of each modeling approach are discussed.