The statistical second-order two-scale method is developed to predicte the mechanical parameters of the composite structure with inconsistently random distribution, including stiffness parameters and elastic limit strength parameters. This kind of structure, in which random inclusion dispersions are not the same everywhere but gradually changing in space, is called the structure with inconsistently random distribution. So, it possesses continuously varying macro-mechanical properties in space. In this paper, the microstructure of the composites with consistently/inconsistently random distributions is represented. The statistical second-order two-scale analysis formulation is established. And the strength criterion of the inconsistent random composite structure is discussed. Finally, the numerical results for different inconsistent composite structures are obtained and compared with the experiment data. Their agreement shows that the statistical second-order two-scale method is feasible to predict mechanical parameters of inconsistently random composites.
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