Micromechanical modeling of non-ageing fractional viscoelastic reinforced composites

In this paper, the non-ageing effective behavior of fractional viscoelastic reinforced composites is predicted based on the Mori-Tanaka approach. The mathematical modeling is based on the Carson-Laplace transform, the dynamic Greens function and the integral equations. Various fractional viscoelastic models can be easily considered. The localization tensors relating local fields and macroscopic ones are derived based on the equivalence inclusion of Eshelby. The Homogenization of the effective behavior is obtained as a function of volume fractions of the constituents and their properties as well as of the volume fraction of reinforcements in the Carson domain.