The paper provides statistical analysis of the photographs of four various granular materials (peas, pellets, triticale, wood chips). For analysis, the (parametric) ANOVA and the (nonparametric) Kruskal-Wallis tests were applied. Additionally, the (parametric) two-sample t-test and (non-parametric) Wilcoxon Rank-Sum Test for pairwise comparisons were performed. In each case, the Bonferroni correction was used. The analysis shows a statistical evidence of the presence of differences between the respective average discrete pixel intensity distributions (PID), induced by the histograms in each group of photos, which cannot be explained only by the existing differences among single granules of different materials. The proposed approach may contribute to the development of a fast inspection method for comparison and discrimination of granular materials differing from the reference material, in the production process.
A two-scale numerical homogenization approach was used for granular materials. At small-scale level, granular micro-structure was simulated using the discrete element method. At macroscopic level, the finite element method was applied. An up-scaling technique took into account a discrete model at each Gauss integration point of the FEM mesh to derive numerically an overall constitutive response of the material. In this process, a tangent operator was generated with the stress increment corresponding to the given strain increment at the Gauss point. In order to detect a loss of the solution uniqueness, a determinant of the acoustic tensor associated with the tangent operator was calculated. Some elementary geotechnical tests were numerically calculated using a combined DEM-FEM technique.