Statistical Approach to the Representative Volume Element Size of Random Composites

This chapter reminds through physical examples the principle of numerical computation of apparent properties. This numerical approach involves a statistical definition of are representative volume element (RVE) to provide intervals of confidence of the estimated apparent properties in the cases of linear and nonlinear constitutive equations. It is illustrated by examples of application to linear and nonlinear micromechanics, optics, fluid flows and wave propagation for various types of microstructures of industrial materials, as well as of models of random media. The plasticity of metallic polycrystals is the subject of many contributions in micromechanics of bulk crystalline solids. The question of RVE size is central in the computation of apparent nonlinear properties of polycrystalline aggregates addressed for the first time in a systematic way. For a nonlinear constitutive behavior, in micromechanics, it is wise to estimate the macroscopic stress–strain relationships with their intervals of confidence and their own statistical RVE sizes, before estimating the parameters of the underlying constitutive equations.