A micro–macro homogenization scheme for elastic composites containing high volume fraction multi-shape inclusions

Abstract

This study aims to obtain mechanical properties of multi-phase composite materials containing high volume fraction of inclusions. To this end, a new method is presented for the homogenization of multi-phase composites. The present homogenization method is developed based on a combination of the Mori–Tanaka model and the modified differential scheme 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. In the second stage, the stiffness tensor for the homogenized material is calculated based on the modified differential scheme model. Then, in the third stage, strain concentration tensor is calculated based on the Mori–Tanaka model as well as Eshelby equations. Finally, in the fourth stage, strain concentration and stiffness tensors for the homogenized material are calculated. For homogenization, according to the shape of the inclusion as well as its volume fraction, the strain concentration tensor is calculated in each stage, and the properties of homogenized material are used in order to calculate the stiffness tensor. Using this method, instead of using mechanical properties of the initial matrix material, properties of the homogenized matrix material are included in each stage of calculations. In this way, the effects of the inclusion on the state of stresses of adjacent inclusions are also considered. This strategy is continuously repeated until the equivalent stiffness tensor is obtained. To validate the new proposed model, an experimental program was conducted and the obtained results were evaluated with the results of experiments.