Simulation of stiffness of randomly-distributed-graphene/epoxy nanocomposites using a combined finite element-micromechanics method

In this study, a new approach was developed for prediction of the stiffness of polymer nanocomposites with randomly distributed graphene sheets. This approach is a combination of the finite element and micromechanics methods. First, the stiffness of the nanocomposites containing one layer of an aligned nano graphene embedded in a polymer was modeled by using a finite element method. The matrix was considered as a continuum phase and each covalent bond of graphene sheet was simulated by an equivalent structural beam. Nonlinear springs were used as Van der Waals bonds in the interphase region of graphene and polymer. Considering the real size of graphene nano platelets, the numerical simulation of the representative volume element of nanocomposites with a real size aligned graphene sheets embedded in the matrix is not a feasible task. Therefore, in the present research, a new approach was developed to overcome this problem. In this new approach, by using the moduli of different graphene sheets with different sizes embedded in a representative volume element, the moduli of a real size graphene embedded in the matrix were predicted. The results obtained by the finite element method were used by the micromechanics approach in order to consider the effect of the random distribution of graphene sheets in a polymer. By combining these two methods, the stiffness of nanocomposites with randomly distributed graphene sheet was predicted. The result of the model is in an acceptable agreement with the result of conducted experimental program.