The multi-scale computational method for the mechanics parameters of the materials with random distribution of multi-scale grains

In this paper, the multi-scale analysis (MSA) method for the mechanics parameter computation of composite materials with random distribution of multi-scale grains is presented. First the representation of the materials with random distribution of multi-scale grains is described. Then the statistically two-scale analysis (STSA) formulation for the composite materials with periodically random distribution of one-scale grains is developed by means of construction approach inside each cell with same probability distribution, and the procedure of statistic MSA computation based on STSA method is discussed in detail. Finally, the numerical results in the model example and application to the engineering are shown. They show that SMSA is feasible to predict the mechanics performance of the materials with random distribution of grains.