A multi-scale cubic model to calculate the elastic modules of the graphene/polymer nano composites

In this paper a new multi-scale method was presented to calculate the elastic modulus of graphene/polymer nano composites. Macro, micro and nano scales were considered within this hierarchical multi-scale method. In macro scale, a nanocomposite was modeled with a cubic representative volume element (RVE) which was constructed by several small cubic elements in micro scale. Each element in micro or nano scale, is made of aligned graphenes which were oriented in three dimensional space via a random algorithm. The stiffness tensor of each element was obtained by Mori-Tanaka micromechanical method and the elastic modulus of the RVE was calculated using a new analytical approach. In fact this method is a development of the laminated analogy, in to a three dimensional version which is in better accordance with the physics of real nanocomposites. It has been shown that the results of the present approach are in good agreement with several experimental works in the literature.