A Definition of Equivalent Inhomogeneity Applicable to Various Interphase Models and Various Shapes of Inhomogeneity

The concept of equivalent inhomogeneity has been introduced to analyze the effective properties of composites with interphases using techniques devised for problems without interphases. The basic idea is to replace the inhomogeneity and the surrounding it interphase by a single equivalent inhomogeneity with constant stiffness tensor, combining properties of both, which is then perfectly boned to the matrix. In this presentation a new definition of equivalent inhomogeneity is discussed. It is based on Hill's energy equivalence principle, applied to the problem consisting only of the original inhomogeneity and its interphase. It is more general than the definitions proposed in the past in that, conceptually and practically, it allows to consider inhomogeneities of various shapes and various models of interphases. This is illustrated considering spherical and cylindrical particles with two models of interphases, Gurtin-Murdoch material surface model and spring layer model. The resulting equivalent inhomogeneities are subsequently used to determine effective properties of randomly distributed unidirectional particulate composites. Properties of the equivalent cylindrical inhomogeneities are transversely isotropic, thus the method of conditional moments, which is a statistical method capable of handling anisotropy and randomness, has been employed for that purpose. Closed-form formulas for the effective stiffness tensor have been developed in all cases considered here. Comparisons with solutions available in the literature are made and other possible applications are discussed.