Determination of RVE size for random composites with local volume fraction variation

In this paper, a novel computational procedure is proposed for the determination of the representative volume element (RVE) size for random composites, which is the basis of homogenization methods. The proposed approach takes into account the local volume fraction variation by processing computer-simulated images of composites with randomly scattered inclusions. A variable number of microstructure models are derived directly from the images using the moving window technique. Each microstructure model contains different amount of inclusions, measured by image analysis tools. The proposed computational procedure is based on the solution of multiple boundary value problems under kinematic and static uniform boundary conditions using the extended finite element method (XFEM) coupled with Monte Carlo simulation (MCS). In this way, the statistical characteristics of the upper and lower bounds of the apparent material properties are computed. The RVE is attained within a prescribed tolerance by examining the convergence of these two bounds with respect to the mesoscale size. The numerical results clearly demonstrate the significant effect of matrix/inclusion stiffness ratio and volume fraction on the convergence rate. The proposed computational procedure leads to RVEs which can give more realistic results when used in homogenization problems. Mesoscale random fields describing the spatial variation of the components of the apparent elasticity tensor are also determined using the proposed approach.