| A general micromechanically-based model is developed in a systematic manner to determine the overall properties of a broad class of linearly elastic composite materials. The composite materials are modeled as infinite solids containing periodically distributed inhomogeneities. In view of the periodicity, the elastic field of the composite material can be expressed in Fourier series. Exact upper and lower bounds on the overall moduli of multi-phase composites are obtained by using the generalized Hashin-Shtrikman variational principles. The interactions among the inhomogeneities are accounted for in an explicit and direct manner. Explicit expressions and numerous examples for two-phase composite materials, including particulate, whisker, and fiber-reinforced composites, are presented. The solution for the extreme case of solids containing periodically cracks is derived by considering flat voids first and then letting the thickness aspect ratio of the void approaching zero. This limiting case is taken with care. In addition to the bounding formulation, two micromechanics models, which are also based on the periodic microstructure and emerge from the bounding solution, are developed to estimate the overall moduli of composite materials. These estimates fall within the bounds. |
