Abstract
A statistical mechanics theory is formulated to capture the effect of microstructure distribution on the effective elastic moduli of a composite material. Two point probability functions are used as a major component of the statistical theory. The statistical correlation functions represent the morphology and the distribution (random, periodic,…) of phases. The theory can benefit from simple mathematical representation of distribution or the shape of the second phase (circular, elliptical,…). A two-point probability function is used to approximate the correlation functions for a general class of geometries with isotropic and random distributions. The simulations are also provided and compared to other (periodic) distributions. The results show that the theory is capable of capturing the microstructural featuring in addition to the statistical distributions.
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