Modeling and Estimating the Effective Elastic Properties of Carbon Nanotube Reinforced Composites by Finite Element Method

Carbon nanotubes (CNTs) possess extremely high stiffness, strength and resilience, and may provide the ultimate reinforcing material for the development of nanocomposites. Evaluating the effective elastic properties of such nanoscale materials is a difficult task. Modelings and simulations using continuum mechanics models can play significant roles in this development. In this paper, the nanostructure is modeled as a linearly elastic composite medium, which consists of a homogeneous matrix having hexagonal representative volume elements (RVEs) and homogeneous cylindrical nanotubes. Formulas to extract the effective elastic constants from solutions for the RVEs under axial as well as lateral loading conditions are derived based on the continuum mechanics approach. An extended rule of mixtures is applied to evaluate the effective Young’s moduli for validation of the proposed model. Numerical examples using the finite element method (FEM) are presented, which demonstrate that the load carrying capacities of the CNTs in a matrix are significant. For the RVEs with long carbon nanotubes, better values of stiffness in the axial direction are found, as compared to stiffness in the lateral direction. Also, a comparative evaluation of both square and hexagonal RVEs with short carbon nanotubes is performed here, which indicates that the hexagonal RVEs may be the preferred models for obtaining more accurate results. Finally, the finite element results are compared with the rule of mixtures using formulae. It is found that the results offered by proposed model, are in close proximity with those obtained by the rule of mixtures.