A Two-Level Homogenization Approach for Polymer Nanocomposites with Coated Inclusions

In polymer nanocomposites, other than the matrix and inclusion, a third phase so-called interphase, is commonly observed. Inter-phase properties affect the overall macroscopic mechanical behavior. It is crucial to model the interphase and obtain the effective composite properties accordingly. Homogenization theory is very useful and powerful; however, many of the homogenization-based techniques have deficiencies. The goal of the study is to combine two very well-known homogenization techniques to model the polymer nanocomposites with coated inclusions. One of the goals of the study is to demonstrate the deficiency that originated from the interphase modeling and overcome this problem by the proposed two-level homogenization method. This method aims to model load transfer between the matrix and the reinforcement element through the interphase in a correctly. For this purpose, first, an effective inclusion is formed using finite element homogenization, then the effective inclusion and the matrix are homogenized using micromechanics-based Double Inclusion method. The proposed method provides a remarkable improvement compared to the micromechanics-based method for the soft interphase case.