Overall viscoelastic response of random fibrous composites with statistically quasi uniform distribution of reinforcements Original Research Article

An accurate representation of time dependent response of polymeric composite systems with disordered microstructure is developed within the framework of classical homogenization methods. In our study, a graphite fiber tow impregnated by an epoxy resin is just an example of such systems. The investigation is focused on modeling issues pertinent to random, non-periodic material systems, while the loading conditions are left to those promoting the linear viscoelastic deformation only. Two different approaches are examined. The first approach assumes a well defined geometry of the fiber arrangement and specific boundary conditions. In the modeling framework, the complicated real microstructure is replaced by a material representative volume element consisting of a small number of particles, which statistically resembles the real microstructure. Periodic distribution of such unit cells is considered and the finite element method is called to carry out the numerical computation. The theoretical basis for the second approach are the Hashin–Shtrikman variational principles. The random character of the fiber distribution is incorporated directly into the variational formulation employing certain statistical descriptors. At the present time the applications are limited to microstructures, which are sufficiently described by the two-point probability function. The presented results support applicability of both methods to the description of viscoelastic behavior of the selected material system.