Statistical continuum mechanics analysis of an elastic two-isotropic-phasecomposite material

A statistical mechanics theory is formulated to capture the effect of micro structure distribution on the effective elastic moduli of a composite mater ial. Two point probability functions are used as a major component of the s tatistical theory. The statistical correlation functions represent the morp hology and the distribution (random, periodic,...) of phases. The theory ca n benefit from simple mathematical representation of distribution or the sh ape of the second phase (circular, elliptical,...). A two-point probability function is used to approximate the correlation functions for a general cl ass of geometries with isotropic and random distributions. The simulations are also provided and compared to other (periodic) distributions. The resul ts show that the theory is capable of capturing the microstructural featuri ng in addition to the statistical distributions. (C) 2000 Elsevier Science Ltd. All rights reserved.