A micromechanical method for particulate composites with finite particle concentration

Many micromechanical models can be obtained by embedding one single ellipsoidal pattern into matrix material to derive localization relation, the direct influence of the other patterns is neglected. An extension of Ponte Castaneda and Willis model (PCW) [J. Mech. Phys. Solids 43 (1995) 1919] to many patterns interaction is proposed for particulate composites with an ellipsoidal distribution of particles. Compared to the models based on one single spherical pattern (Mori-Tanaka model [Acta Metall. 21 (1973) 571] for an isotropic composite) or based on one single ellipsoidal pattern (PCW model for an transverse isotropic composite due to ellipsoidal distribution of particles), the proposed method gives better prediction on the overall elastic properties for particulate composites with finite particle concentration. The extension of the elastic results directly to plasticity are performed with the help of secant moduli method based on second-order stress moment, the prediction on the overall elastic and plastic properties for particulate composites agrees well with the experimental results in literature.