Quantitative description and numerical simulation of random microstructures of composites and their effective elastic moduli

A digital image processing technique is used for measurement of centroid coordinates of fibers with forthcoming estimation of statistical parameters and functions describing the stochastic structure of a real fiber composite. Comparative statistical analysis of the real and numerically simulated structure are performed. Accompanying of known methods of the generation of random configurations by the random shaking procedure allows creating of the most homogenized and mixed structures that do not depend on the initial protocol of particle generation. We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing a statistically homogeneous set of ellipsoidal inclusions. The multiparticle effective field method (see for references, Buryachenko, Appl. Mech. Rev., (2001a), 54, 1–47) based on the theory of functions of random variables and Green’s functions is used for demonstration of the dependence of effective elastic moduli of fiber composites on the radial distribution functions estimated from the real experimental data as well as from the ensembles generated by the method proposed.