The linking of microstructure uncertainty with the random variation of material properties at the macroscale is particularly needed in the framework of the stochastic finite element method (SFEM) where arbitrary assumptions are usually made regarding the probability distribution and correlation structure of the macroscopic (effective) mechanical properties. In this work, the linking is efficiently accomplished by exploiting the excellent synergy of the extended finite element method (XFEM) and Monte Carlo simulation for the computation of the effective properties of random two-phase composites. The homogenization is based on Hill's energy condition and involves the generation of a large number of realizations of the microstructure with uncertainty in the geometry (shape, number, spatial distribution and orientation of inclusions) or in the constituent material properties. The mean value, coefficient of variation and probability distribution of the effective elastic modulus and Poisson ratio of the random composite are computed. A comparison of the relative influence of the above two kinds of uncertainty is made. The effective properties are finally used in the framework of SFEM to obtain the response of a composite structure and useful conclusions are derived regarding the effect of random microstructure on the probabilistic characteristics of the response.

This work is supported by the European Research Council Advanced Grant ''MASTER-Mastering the computational challenges in numerical modeling and optimum design of CNT reinforced composites'' (ERC-2011-ADG 20110209).