Three-dimensional micromechanical modeling of effective elastic properties of GNP-reinforced polymer nanocomposite considering the GNP size and agglomeration

A three-dimensional analytical micromechanical model based on the unit cell is extended to extract the elastic properties of GNP-reinforced polymer nanocomposites. GNP/matrix interphase region changing gradually and is considered elastic with isotropic behavior. In order to simulate the random distribution of GNPs, the geometry of the representative volume element of the nanocomposite is divided into a three-dimensional cubic with N_α×N_β×N_γ subcells. First, the obtained results are compared with the available researches. Then, the effect of parameters such as the volume fraction and aspect ratio of GNPs, the effect of agglomeration as well as the random distribution of GNPs in the epoxy resin, and the thickness of the interphase on the response of the nanocomposite are investigated. It is shown that the agglomeration of GNP depends on its volume fraction. The results show that the elastic properties obtained from the present micromechanical model with taking into account the random distribution and the agglomeration of nanoparticles and also interphase are close to the experimental data. According to the obtained results, adding even a small volume fraction of GNPs has a significant effect on improving the properties of the nanocomposite. In addition, the modeling of the interphase region also has a great impact on the properties of the nanocomposite. Therefore, in order to realistically predict the behavior of nanocomposites, it is important considering to the interphase.