Size of RVE in random micropolar composites

The worldwide concern for the stewardship of old structures and gems of ancient architecture calls for multiscale mechanics models of walls built of stones with random properties and shapes. While the walls of periodically structured masonry have already successfully been modeled by Cosserat (micropolar) continua, the presence of disorder requires development of random micropolar continua, where one has to determine the finite-size scaling from a Statistical Volume Element (SVE) to a Representative Volume Element (RVE). To this end, we use the recently established macrohomogeneity (Hill-Mandel type) condition accounting for couple-stress and curvature-torsion tensors besides the conventional Cauchy stressses and strains. Overall, the RVE is approached in terms of two hierarchies of bounds stemming, respectively, from Dirichlet and Neumann boundary value problems set up on the SVE. In particular, we focus on composite materials with a random, non-periodic internal structure of Cosserat type. Various combinations of matrix (mortar) and inclusion phases (stones) are examined and a stochastic study is carried out in order to extract the "averaged" homogenized constitutive properties for a fixed control window (mesoscale). Once the RVE size is determined as a function of the internal length of the material, the converged homogenized constitutive parameters are obtained and are used for large scale numerical simulations on 2D masonry panels. Since the micropolar model is richer than a corresponding one for a local medium, it is characterized by a higher number of constitutive parameters. This methodology then forms a rational basis for setting up of mesoscale continuum random fields and stochastic finite element methods.