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A random field model for generating synthetic microstructures of functionally graded materials

This article presents a new level‐cut, inhomogeneous, filtered Poisson random field model for representing two‐phase microstructures of statistically inhomogeneous, functionally graded materials with fully penetrable embedded particles. The model involves an inhomogeneous, filtered Poisson random field comprising a sum of deterministic kernel functions that are scaled by random variables and a cut of the filtered Poisson field above a specified level. The resulting level‐cut field depends on the Poisson intensity, level, kernel functions, random scaling variables, and random rotation matrices. A reconstruction algorithm including model calibration and Monte Carlo simulation is presented for generating samples of two‐phase microstructures of statistically inhomogeneous media. Numerical examples demonstrate that the model developed is capable of producing a wide variety of two‐ and three‐dimensional microstructures of functionally graded composites containing particles of various sizes, shapes, densities, gradations, and orientations. An example involving finite element analyses of random microstructures, leading to statistics of effective properties of functionally graded composites, illustrates the usefulness of the proposed model. Copyright © 2008 John Wiley & Sons, Ltd.