A statistical micromechanical multiscale method for determination of the mechanical properties of composites with periodic microstructure

In the current research a statistical micromechanical approach for the determination of the mechanical properties of composite materials is proposed. The proposed method is mainly based on the well-known periodic homogenization scheme. The methodology implements multi-step multiscale approach to calculate the mechanical properties of composite materials where the statistical characteristics (e.g. size, aspect ratio, orientation) of the reinforcing phase are known as probability distribution functions (PDF). The calculations start from Unit Cell I which resembles the microstructure of material at the lowest length scale and continue until the largest fiber is considered in the final unit cell setting. The results of the presented theory are compared with experimental data on composite materials which show that good estimates of the elastic moduli can be achieved by using statistical multi step homogenization technique.