Statistical moments for random two-phase suspensions: A computational framework

Abstract

A new method for decomposing multipoint correlation functions is presented for two-phase suspension materials. The decomposition isolates various aspects of the substructure geometry such as inclusion shape and relative sizes, orientations, and positions of the inclusions. The method can be systematically applied to correlation functions of any order, and it allows them to be calculated directly from a given suspension substructure geometry. First the material properties of the phases are separated from the substructure geometry and this latter is described in terms of the inclusion phase alone. Second the geometric probabilities associated with the inclusion phase are separated into the probabilities associated with the individual inclusions taken singly, and in groups of two or more. The single inclusion probability is given by a geometry problem which is to be solved analytically (or numerically) for a given inclusion shape and orientation. The double inclusion probability, triple inclusion probability, etc., separate into (1) a probability function which depends on inclusion shape, size, and orientation; its calculation is reduced to a geometry problem like that of the single inclusion probability, and (2) inclusion distribution functions which contain configuration statistics.