Characterization and identification of the memory decay rates of carbon black-filled rubber

This paper is concerned with the identification of the dynamic moduli of viscoelastic constitutive models on the basis of a nonlinear optimization method by fitting data on carbon black-filled rubber. The models considered can be categorized in two different classes according to the definition of the relaxation function: models whose kernel decays exponentially fast, e.g., Debye model, and non-Debye relaxation spectra with a slower decay rate of the viscoelastic kernel, e.g., Cole-Cole model. On the basis of a recent result (Ciambella, Paolone, & Vidoli 2011), we show that all the kernels whose decay rate istoo fast lead toidentification problems which are, in general, ill-conditioned. This shortcoming, in turn, manifests itself in the presence of multiple sets of optimal parameters for the same data sets. Moreover, this multiplicity can lead to very different constitutive responses when extrapolating material behaviour outside the range of the experimental data.