Homogenization of inelastic composites with misaligned inclusions by using the optimal pseudo-grain discretization

The paper deals with micromechanics of composite materials reinforced with misaligned, non-spherical inclusions. The main goal of this study is focused on numerical treatment of misaligned orientations by using the concept of two-step homogenization. The paper is concerned with the novel method of pseudo-grain discretization based on the optimal selection of pseudo-grains discrete orientations and corresponding weights. In order to solve the optimization problem evolutionary algorithms are used. The proposed approach leads to reduction of the pseudo-grains amount which, in turn, especially in the case of inelastic materials, results in homogenization that is more computationally efficient. The accuracy of the proposed method is presented by analysis of exemplary microstructures. Both the orientation data reconstruction accuracy and stiffness prediction accuracy are discussed. In addition, cases of elastic-plastic material behaviour are analysed and two-step homogenization results are compared with results of direct finite element (FE) based homogenization of representative volume element (RVE) with complex geometry.