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The macroscopic mechanical and physical properties of heterogeneous materials can be efficiently determined using either analytical or numerical homogenization techniques where the identification of a representative volume element (RVE) is required over which a fine-scale boundary value problem is solved. In this work, an efficient computational scheme is proposed 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. A variable number of microstructure models are directly constructed by segmentation of the composite material image into windows of certain size. The proposed numerical procedure takes into account the particle volume fraction variation through digital image processing of the microstructure models. The proposed approach couples the extended finite element method (XFEM) with 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 window size. The XFEM analysis of the microstructure models also leads to upper and lower bounds for their constitutive behavior by solving Dirichlet and Neumann boundary value problems. The RVE is attained within a prescribed tolerance by examining the convergence of these two bounds with respect to the mesoscale size and useful conclusions are derived about the effect of matrix/inclusion stiffness ratio as well as of inclusion volume fraction on the apparent properties and on the RVE size.

DETERMINATION OF MESOSCALE RANDOM FIELDS FOR THE APPARENT PROPERTIES OF SPATIALLY RANDOM COMPOSITES