Elastic field and effective moduli of periodic composites with arbitrary inhomogeneity distribution

This paper develops a semi-analytic model for periodically structured composites, of which each period contains an arbitrary distribution of particles/fibers or inhomogeneities in a three-dimensional space. The inhomogeneities can be of arbitrary shape and have multiple phases. The model is developed using the Equivalent Inclusion Method in conjunction with a fast Fourier Transform algorithm and the Conjugate Gradient Method. The interactions among inhomogeneities within one computational period are fully taken into account. An accurate knowledge of the stress field of the composite is obtained by setting the computational period to contain one or more structural periods of the composite. The effective moduli of the composite are calculated from average stresses and elastic strains. The model is used to analyze the stress field and effective moduli of anisotropic composites that have cubic symmetry. It shows that the bulk and shear moduli predicted by the present model are well located within the Hashin-Shtrikman bounds. The study also shows that the stress field of the composite can be significantly affected by the distribution of inhomogeneities even though the effective moduli are not affected much.