The statistical second-order two-scale analysis method for heat conduction performances of the composite structure with inconsistent random distribution

In this paper, a statistical second-order two-scale (SSOTS) method is presented for predicting heat conduction performances of the structures of composite materials with inconsistent random distribution. Firstly, the meso-scopic configuration for the structure with inconsistent random distribution is characterized. Secondly, the SSOTS asymptotic formulation for predicting the heat conduction parameters and the temperature fields of the heat conduction problems of the structure is given by means of construction way. Then the heat conduction properties for the functional gradient materials (FGM) with varying volume fraction are predicted by the SSOTS method. The numerical results are compared with experimental data and theoretical results. Finally, macroscopic heat conduction properties for the structures with varying probability distribution models including size, location and orientation distributions of grains are calculated. The numerical results show that the SSOTS method in this paper is valid to predict heat conduction performances of composite structures with inconsistent random distribution.