Stochastic finite element analysis of composite structures based on mesoscale random fields of material properties

The linking of microstructure uncertainty with the random variation of material properties at higher scales is of paramount importance in the framework of the stochastic finite element method (SFEM). An efficient computational scheme has been recently proposed by the authors for the determination of mesoscale random fields for the apparent properties and of the RVE size of particle-reinforced composites based on computer-simulated images of their microstructure. The proposed approach exploits the excellent synergy of the extended finite element method (XFEM) and Monte Carlo simulation in order to analyze the microstructure models and obtain statistical information (probability distribution, correlation structure) for the apparent properties of the composite in each mesoscale size. In this paper, sample functions of the statistically homogeneous mesoscale random fields are generated using the spectral representation method in conjunction with translation field theory. Moreover, micro-mechanically consistent (lower and upper) bounds on the macroscopic response of composite structures are computed in the framework of SFEM. Useful conclusions are derived regarding the effect of particle/matrix stiffness ratio on the probabilistic characteristics of the mesoscale random fields as well as the influence of mesoscale size on the response variability.