Mathematical modeling of fractional visco-electroelastic composites using regularized micromechanical methods

Abstract

In this paper, mathematical modeling and numerical formulations are developed to predict the overall behavior of fractional visco-electroelastic composites. The modeling is based on Riemann-Liouville's fractional derivative formulation, Carson-Laplace transform, the frequency Green's functions, and integral equation formulations. The micro-macro modeling is elaborated for various heterogeneous visco-electroelastic composites. The inclusion problem and a micromechanical method are used to obtain the localization and the concentration tensors expressions. The block decomposition procedure is used to address the draw-back of the ill-conditioned problem caused by the localization tensor inverses. The effective fractional visco-electroelastic behavior is expressed based on the regularized concentration tensor and the Mori-tanaka method. Numerical results of effective fractional visco-electroelastic properties are obtained and examined for various fractional parameter, volume fraction and shapes of inclusions in frequency domain.