A novel model for homogenization of multi-phase composites with high volume fraction of inclusions

This study aims to obtain mechanical properties of multi-phase composite materials with high volume fraction of inclusion. For this purpose, a new method is presented for the homogenization of multi-phase composites. A new homogenization method was developed based on a combination of the Mori-Tanaka model and the differential model. The new homogenization method was named MT-DS model which consists of four stages. In the first stage, average strain created in the inclusion is calculated. Then, based on the modified differential scheme, the stiffness tensor for the homogenized material is calculated. In the third stage, based on the Mori-Tanaka model as well as Eshelby equations, the strain concentration tensor is calculated. Finally, in the fourth stage, using the MT-DS model, the strain concentration and stiffness tensors for the homogenized material are calculated. For homogenization, according to shape of the inclusion as well as its volume fraction, the strain concentration tensor is calculated and the homogenized material is used in order to calculate the stiffness tensor. Using this method, in each stage, instead of properties of the raw matrix material, properties of the homogenized matrix material are included in the calculations. The effect of other inclusions on the adjacent inclusions is also considered. This procedure is continuously repeated until the equivalent stiffness tensor is obtained. To validate the new proposed model, obtained results were evaluated in a comparison with the results of the experiments.