Multiscale modeling of the elastic moduli of CNT-reinforced polymers and fitting of efficiency parameters for the use of the extended rule-of-mixtures

In this work, a bottom-up multiscale modeling approach is developed to estimate the effective elastic moduli of Carbon NanoTube (CNT)-reinforced polymer composites. The homogenization process comprises two successive steps, including an atomistic-based computational model and a micromechanics approach at the nano- and micro-scales, respectively. Firstly, the atomistic-based finite element model defines a cylindrical Representative Volume Element (RVE) that accounts for a carbon nanotube, the immediately surrounding matrix, and the CNT/polymer interface. The carbon-carbon bonds of the CNT are modeled using Timoshenko beams, whilst three-dimensional solid elements are used for the surrounding matrix. Through the application of four loading conditions, the RVEs are homogenized into transversely isotropic equivalent fibers by equating the associated strain energies. Secondly, the equivalent fibers are employed in a micromechanics approach to estimate the macroscopic response of non-dilute composites. This is performed using both the analytical Mori-Tanaka model and a computational RVE model with a hexagonal packing geometry. A wide spectrum of single- and multi-walled carbon nanotubes are studied, as well as two different polymeric matrices. Furthermore, the so-called efficiency parameters, imperative for the application of the simplified extended rule of mixtures, are characterized by polynomial expressions for practical filler contents. Finally, detailed parametric analyses are also provided to give insight into the sensitivity of the macroscopic response of CNT-reinforced polymer composites to microstructural features such as filler volume fraction, chirality or aspect ratio.