Chapter Eleven - Computational Homogenization of Anisotropic Carbon/Rubber Composites With Stochastic Interface Defects

Abstract

The main goal of this study is stochastic homogenization of the carbon/rubber composites reinforced with nonuniformly distributed carbon black (CB) particles in the cubic representative volume element (RVE). This is done to determine the anisotropic random effective elasticity tensor of this composite and its first four probabilistic characteristics, i.e., expected values, coefficients of variation, skewness, and kurtosis. The multiparticle RVE is composed of three domains—matrix, 27 CB spherical particles and the interphases—where the stochastic defects are modeled by the semispheres lying on the particle–matrix interface. They are replaced further by probabilistically averaged stiffness characteristics of the equivalent elastic interphase and incorporated into computational experiments consisting of the finite element method error analysis, sensitivity assessment, and probabilistic study of the effective stiffness tensor—the triple approach includes stochastic perturbation method, Monte Carlo simulation, and semianalytical approach. The input Gaussian random variable is defined as the volume fraction of the interface defects w by using its dispersion α(w) as well as its expected value E(w).