Stochastic modeling and analysis of porous media using first-order perturbation-based homogenization method

A stochastic analysis of multi-scale problem in porous media was introduced in this paper to determine the variation of macroscopic homogenized properties considering uncertainties at microscopic level. By assuming the small fluctuation that arises in microscopic properties was distributed in Gaussian normal distribution, the macroscopic homogenized properties has been formulated in stochastic manner using first-order perturbation-based. The merit of this method lies in the ability to consider other uncertainties instead of microscopic properties due to random microstructure variations. Hence, the proposed stochastic homogenization method was established by adding two demonstrative problems that commonly occur in engineering materials. First, the fluctuation of Young's modulus in adhesive of two-phase materials was considered to demonstrate a simple numerical model that can predict the dispersion of macroscopic properties. Next, the variation in microscopic properties was combined with misalignment of stacked plate microstructure to investigate the effects on macroscopic properties of corrugated-core. The results showed that the misaligned position in some distances increased the macroscopic properties but by taking the probability function on misalignment reduced that. It proved that the significance of this study in design and fabrication of porous media considering random variation of microstructure.