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This paper investigates the validity of two different analytical homogenization methods: the Mori–Tanaka mean-field theory and Milton’s correlation function-dependent bounds. We focus on biphase linearly elastic transversely isotropic composites. The composites consist of a matrix reinforced with long fibers of either circular or irregular cross section shapes formed by overlapping circles, with different degrees of radius polydispersity. The Mori–Tanaka effective stiffness depends on the phase moduli, volume fractions, and on a few geometric descriptors of the fibers that can be readily evaluated. In contrast, the computation of Milton’s bounds requires finer knowledge of the microstructure, in terms of two and three-point spatial correlation functions, which are not always analytically tractable. We thus consider very specific random microstructure geometries with known correlation functions. The effective moduli estimates of the two methods are validated against the results of numerical homogenization using the finite element method. It is shown that the Mori– Tanaka predictions of the effective transverse bulk modulus are significantly more accurate than those of the transverse and axial shear moduli. In addition, the predictions of the scheme generally deteriorate with an increasing fiber volume fraction. By contrast, the average of Milton’s upper and lower bounds provides a highly accurate estimate for all three independent effective moduli, without any limitation on the fiber concentration. This study highlights the indisputable effect of the spatial correlation functions on the effective properties of composites, and aspires to pave the way towards the development of more predictive, correlation function-dependent homogenization methods. 

The representation of material microstructure in most existing analytical homogenization models is condensed into a set of well-known ‘‘classical’’ microstructure descriptors, such as the volume fraction and morphology of the individual phases of a composite. This study considers an enriched set of micro descriptors, containing both those ‘‘classical’’ descriptors as well as ‘‘non-classical’’ descriptors which quantify the spatial correlations of any two given micro material points inside a random heterogeneous material. We focus on 2D composites consisting of a matrix with embedded inhomogeneities (or inclusions) of random spatial arrangement. Both phases are treated as homogeneous, linearly elastic and isotropic. Starting from a rich database of reference microstructures, new datasets of perturbed microstructures are created, by inducing changes emulating the physical processes of inclusion nucleation and growth. All microstructures are characterized using the enriched set of micro descriptors, while their apparent stiffness tensor is computed numerically with the finite element (FE) method. A sensitivity analysis between the changes of the micro descriptors and corresponding changes of the apparent stiffness tensor reveals that the ‘‘non-classical’’ descriptors are consistently highly important to the macroscopic behavior. This suggests that enhanced homogenization models, made dependent on the identified pertinent ‘‘non-classical’’ micro descriptors, could be of higher predictive capability than existing approaches.