A novel multiscale method for mechanical properties of statistically inhomogeneous materials

This paper develops a novel multiscale method to predict mechanical performance of statistically inhomogeneous materials. As for these kinds of materials, the sophisticated microscopic information of inclusions, including their shape, size, orientation, spatial distribution, volume fraction and so on, leads to changes of the macroscopic mechanical properties. The multiscale formulae for solving the mechanical problems are proposed, and the associated prediction algorithm based on the two-scale model is brought forward in detail. Finally, some numerical results for the effective properties of the materials with varying probability distribution models are calculated by the algorithm proposed, and compared with the data by experimental results.