STOCHASTIC MULTISCALE MODELING OF TWO-PHASE MATERIALS BASED ON FIRST-ORDER PERTURBATION METHOD

The homogenization method has been well established in multiscale engineering practise to determine the effective elastic constants of linear elasticity of heterogeneous materials by considering their microstructure. This method was developed to reflect the microscopic structure without looking at details of all of the material points of the body, whenever the mechanical behaviour of the macroscopic body is in question. Nevertheless, in the classical homogenization method, the microscopic characteristics were modelled in deterministic manner. To estimate the expectation and dispersion of macroscopic properties considering uncertainties in micro structure caused by distributing properties of constituent materials, variations in geometry and so on, expensive calculation should be repeated supposedly many times using Monte Carlo simulation. Therefore, this study aims to predict the macroscopic properties of two-phase materials considering uncertainties in microstructure by introducing the stochastic multiscale method. Stochastic finite element method using first-order perturbation-based was combined with homogenization theory to derive the formulation. By assuming the fluctuation arises in microscopic property is distributed in normal distribution, determination of macroscopic properties was formulated in stochastic treatment. Then, the proposed method was established by adding some demonstrative examples that commonly occurred in engineering materials. The numerical results suggest that the uncertainties in microstructure influenced the macroscopic properties of two-phase materials. It indicates the importance of presented stochastic multiscale analysis for micro structure design with considering the microscopic random variations.