Analysis of Fractional Viscoelastic Material With Mechanical Parameters Dependent on Random Temperature

It is well known that mechanical parameters of polymeric materials, e.g., epoxy resin, are strongly influenced by the temperature. On the other hand, in many applications, the temperature is not known exactly during the design process and this introduces uncertainties in the prevision of the behavior also when the stresses are deterministic. For this reason, in this paper, the mechanical behavior of an epoxy resin is characterized by means of a fractional viscoelastic model at different temperatures; then, a simple method to characterize the response of the fractional viscoelastic material at different temperatures modeled as a random variable with assigned probability density function (PDF) subjected to deterministic stresses is presented. It is found that the first- and second-order statistical moments of the response can be easily evaluated only by the knowledge of the PDF of the temperature and the behavior of the parameters with the temperature. Comparison with Monte Carlo simulations is also performed in order to assess the accuracy and the reliability of the method.