Overall viscoelastic response of random fibrous composites
with statistically uniform distribution of reinforcements
by
M. Sejnoha and J. Zeman
Abstract
An accurate representation of time dependent response of polymeric composite systems
with disordered microstructure is developed within the framework of classical homogenization
methods. A graphite fiber tow impregnated by an epoxy resin, Fig.~\ref{F1}(a), 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.
Last modified: Dec 12 2001