Stochastic FE-BE method for homogenization analysis of 2D diffusion problems considering uncertainties of inclusion shape

Abstract

The stochastic method for homogenization analysis of diffusion problems considering uncertainties of inclusion shape is developed using a microscopic spectral stochastic BEM and a macroscopic FEM. The spatial variation of inclusion shape is modeled using KarhunenLoeve expansion with exponential-type covariance kernels. The characteristic function on a 2-D unit cell and the homogenized diffusion tensor are calculated using the spectral stochastic BEM. The macroscale diffusion problems are solved using the stochastic FEM with the polynomial chaos (PC) expansion. Through numerical tests, the expected value and the standard deviation of the concentration in macroscale problems and their distribution are investigated.

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