Square representative volume elements for evaluating the effective material properties of carbon nanotube-based composites

Carbon nanotubes (CNTs) demonstrate unusually high stiffness, strength and resilience, and may become an ideal reinforcing material for new nanocomposites. However, much work has to be done before the potentials of CNT-based composites can be fully realized. Evaluating the effective material properties of such nanoscale materials is one of many difficult tasks. Simulations using molecular dynamics and continuum mechanics models can play significant roles in this development. Currently, the continuum approach seems to be the only feasible approach for such large scale analysis. In this paper, effective mechanical properties of CNT-based composites are evaluated using a square representative volume element (RVE) based on the continuum mechanics and with the finite element method (FEM). Formulas to extract the effective material constants from solutions for the square RVEs under two load cases are derived based on the elasticity theory. Numerical results using the FEM show that the load carrying capacities of the CNTs in a matrix are significant. For example, with the addition of CNTs in a matrix at a volume fraction of 3.6%, the stiffness of the composite can increase as much 33% in the axial direction with long CNTs. These simulation results are consistent with the experimental results reported in the literature and the earlier results using cylindrical RVEs.