Two-point Probability Function Research Articles

Two-point matrix probability function for two-phase random media: Computer simulation results for impenetrable spheres

Computer simulation results are reported for the two-point matrix probability function S2 in two-phase random, homogeneous systems composed of completely impenetrable spheres. The results compare favorably with the earlier analytic predictions of S2 made by Torquato and Stell.

Effective Properties Of Statistically Homogeneous Random Composites

Macroscopic thermoelastic constitutive equations are derived for random fibrous composite systems with statistically homogeneous distribution of fibers. In particular, the graphite fiber tow embedded in the polymer matrix is selected here as a representative of the two-phase disordered composite media. Random character of fibers arrangement, typical for such material systems, is conveniently described by the two-point probability function. When used with the Hashin-Shtrikman variational principles this function provides sufficient information for obtaining bounds on the thermo-elastic material properties of real composites with statistically homogeneous microstructure. A suitable method to solve the resulting integral equations is proposed.