Experimental and numerical study of elastic behavior of heterogeneous model materials with spherical inclusions

The elastic properties of multi-phased materials have been studied in many papers, mainly focused on the analytical aspect of the problem (Voigt, Reuss, Hashin and Shtrikman...). For a few years, the large diffusion of FEM software offers, beside the analytical and experimental approaches, a new popular way to characterize the behavior laws of such materials. This work deals with two-phase model materials (spherical alumina inclusions in a vitreous matrix) whose linear elastic behaviors were determined by using the three previous approaches: analytical, experimental and numerical. Samples were elaborated with both various and controlled contents in second phase. The process consisted in determining their overall elastic characteristics starting from numerical 2D models, respecting the stereological relationships used in image analysis. After validation by comparison of the values obtained using four FEM software, the results were confronted with those given by analytical models so as with experimental ones. For the studied materials, experimental and numerical results are close to the lower bound of the Hashin and Shtrikman’s model.