A stochastic micromechanical model for elastic properties of functionally graded materials

A stochastic micromechanical model is presented for predicting probabilistic characteristics of elastic mechanical properties of an isotropic functionally graded material (FGM) subject to statistical uncertainties in material properties of constituents and their respective volume fractions. The model involves non-homogeneous, non-Gaussian random field representation of phase volume fractions and random variable description of constituent material properties, a three-phase Mori–Tanaka model for underlying micromechanics and homogenization, and a novel dimensional decomposition method for obtaining probabilistic descriptors of effective FGM properties. Four numerical examples involving statistical properties of input random fields, limited experimental validation, and the second-moment characteristics and probability density functions of effective mechanical properties of FGM illustrate the proposed stochastic model. The results indicate that the model provides both accurate and computationally efficient estimates of probabilistic characteristics of effective FGM properties.