A stochastic analysis of multi-scale problem in honeycomb microstructure was introduced in this paper to determine the variation of macroscopic homogenized properties considering uncertainty of micro-property. By assuming the fluctuation of micro-property, specifically the Young's modulus, is in Gaussian normal distribution, the macroscopic (homogenized) properties was formulated in stochastic manner based on first order perturbation approach. Next, the macroscopic property of honeycomb microstructure considering the geometrical defect that might be occurred in manufacturing process was also predicted. The numerical results showed that even with minor geometrical defect could affect the macroscopic properties. It proved the essential of stochastic homogenization method in predicting the reliable macroscopic property for microstructure design.
A Higher Order Perturbation Approach for Electromagnetic Scattering Problems on Random Domains
