A modified strong-contrast expansion for estimating the effective thermal conductivity of multiphase heterogeneous materials
Al-Haik, Marwan S.
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To evaluate the effective thermal conductivity of a general anisotropic multiphase microstructure, a modified version of statistical strong-contrast expansions is formulated here. The proposed method takes into account the shape, orientation, and distribution of each phase through two-point and three-point correlation functions. By applying a recently developed method, three-point correlation functions are approximated from the two-point correlation functions. Numerically, it is shown that for high contrast constituents, the solution of the third-order strong-contrast expansions is very sensitive to the selection of the reference medium. A technique is proposed to minimize the sensitivity of the solution. To establish the validity of the methods developed, the effective thermal conductivity of a number of isotropic and anisotropic two-phase and three-phase microstructures is evaluated and compared to their corresponding finite element (FE) simulations. Good agreement between the FE simulations and the proposed method predictions in the cases studied confirms its validity. When there are orders of magnitude disparity between the properties of the constituents, the developed method can be applied to better estimate the effective thermal conductivity of the multiphase heterogeneous materials in comparison with previous strong contrast model and other homogeneous methods. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4768467]