A novel finite element model for predicting the effective mechanical performances of graphene nanoplatelets and carbon nanotubes synergistically reinforced polymer nanocomposites

Abstract Graphene nanoplatelets (GNPs) and carbon nanotubes (CNTs) reinforced polymer nanocomposites have received great attention in the fields of aeronautics and astronautics due to their superior comprehensive performances. However, the random distribution configuration of GNPs and CNTs is complicated at the microscale and their synergistic strengthening mechanism is not disclosed clearly. Therefore, it is valuable to predict the equivalent elastic performances of nanocomposites by proposing a new high‐efficient mechanical model. First, this study proposes a new geometrical unit cell model describing the randomly distributed features of GNPs and CNTs by adopting an efficient nanofiller generation algorithm. Then, a micromechanical finite element model for predicting the effective elastic properties of nanocomposites is established by employing the periodical displacement boundary conditions. Especially, the effects of unit cell dimension and sample size on the predicted elastic constants are discussed from the perspective of probability and statistics in detail. To validate the effectiveness of the presented model, the effective elastic constants of GNPs and CNTs reinforced nanocomposites are analyzed, and good agreement is obtained between the predicted values and the available experimental results. The effects of nanofiller mass fraction and mass ratio on the mechanical properties are discussed, and the synergistic strengthening mechanism of GNPs and CNTs is studied in detail. The presented model contributes to conducting the optimization design of GNPs and CNTs reinforced polymer nanocomposites. Highlights Microscale modeling of GNPs and CNTs is crucial for the mechanical appraisal of nanocomposites. Unit cell dimension should be greater than 2500 nm and sample size is greater than 3. Periodical boundary conditions ensure obtaining accurate mechanical response of the unit cell. The elastic properties increase linearly with the increasing mass fraction of nanofillers. Synergistic strengthening mechanism of GNPs and CNTs on elastic properties is revealed.