Assessment of the effect of microstructural uncertainty on the macroscopic properties of random composite materials

The linking of microstructural uncertainty with the random variation in the response of heterogeneous structures at the macroscale is particularly important in the framework of the stochastic finite element method. In this work, the effect of uncertainty in the constituent material properties and the geometry of the microstructure, on the macroscopic properties of composite materials is assessed through computational homogenization. Based on Hill-Mandel homogeneity condition, the homogenization procedure utilizes the excellent synergy of the extended finite element method and the Monte Carlo simulation. In this way, the computation of the statistical characteristics of the homogenized elasticity tensor of random composite materials reinforced with arbitrarily shaped inclusions is performed in a computationally efficient manner. The effect of stochastic variation in the elastic properties of the constituents as well as the effect of inclusion shape on the statistical characteristics of the homogenized elasticity tensor is assessed through probabilistic sensitivity analysis. A comparison is performed with regard to the relative influence of material and geometrical uncertainty which are considered separately. More realistic results are obtained by considering simultaneously material and geometrical uncertainty in the microstructural modeling of composite materials. The results can be further exploited in the stochastic finite element analysis of composite structures where material properties with random characteristics obtained by the presented multiscale homogenization procedure will be assigned to each finite element.