Computation of the relaxation and creep functions of elastomers from harmonic shear modulus

The purpose of this paper is to compute the relaxation and creep functions from the data of shear complex modulus, G∗(iν). The experimental data are available in the frequency window ν∈[νmin ,νmax ] in terms of the storage G′(ν) and loss G″(ν) moduli. The loss factor \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\eta( \nu) = \frac{G''( \nu )}{G'(\nu )}$\end{document} is asymmetrical function. Therefore, a five-parameter fractional derivative model is used to predict the complex shear modulus, G∗(iν). The corresponding relaxation spectrum is evaluated numerically because the analytical solution does not exist. Thereby, the fractional model is approximated by a generalized Maxwell model and its rheological parameters (Gk,τk,N) are determined leading to the discrete relaxation spectrum G(t) valid in time interval corresponding to the frequency window of the input experimental data. Based on the deterministic approach, the creep compliance J(t) is computed on inversing the relaxation function G(t).