Effective elastic properties of the graphite-epoxy unidirectional fiber composite with fibers randomly distributed within the transverse plane section are found. To enhance the efficiency of numerical analysis 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. First, various statistical descriptors suitable for the microstructure characterization of a
random media are considered. Several methods for the determination of these descriptors are proposed and tested for some simple theoretical models of microstructures. Moreover, a validity of various statistical hypotheses usually accepted for a random heterogenous media is checked for the present material as well. Successively, the unit cell is derived from the optimization procedure formulated in terms of these statistical descriptors. A variety of deterministic as well as stochastic optimization
algorithms is examined to solve this problem. It is shown that for this particular application stochastic method based on genetic algorithm combined with the simulated annealing method is superior to other approaches. Finally, the estimates of elastic properties are found for the resultant unit cells using the Finite Element Method. Results suggest that the proposed approach, which effectively exploits the knowledge of material's statistics of the composite, is more reliable then various averaging techniques or simple unit cell models based on the regular fiber distribution.
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