Stochastic homogenized effective properties of three-dimensional composite material with full randomness and correlation in the microstructure

•Analytical homogenization with uncertainty in microstructure.•Fully considering the uncertainty including the randomness and correlation in microstructure.•Random effective properties of a unidirectional fiber reinforced polymer composite.•Random factor method.•Monte-carlo method.

In this work, random homogenization analysis for the effective properties of composite materials with unidirectional fibers is addressed by combining the equivalent inclusion method with the Random Factor Method (RFM). The randomness of the micro-structural morphology and constituent material properties as well as the correlation among these random parameters are fully considered, and stochastic effective properties including effective elastic tensor and effective elastic properties together with their correlation are sought. Results from the RFM and the Monte-Carlo Method (MCM) are compared, and the impact of randomness and correlation of the micro-structural parameters on the random homogenized results are investigated by the two methods. Finally, the correlation coefficients of the effective properties are obtained by the MCM. The RFM is found to deliver rapid results with comparable accuracy to the MCM approach.