Evaluations of the effective material properties of carbon nanotube-based composites using a nanoscale representative volume element

Carbon nanotubes (CNTs) possess extremely high stiffness, strength and resilience, and may provide the ultimate reinforcing materials for the development of nanocomposites. In this paper, the effective mechanical properties of CNT-based composites are evaluated using a 3-D nanoscale representative volume element (RVE) based on continuum mechanics and using the finite element method (FEM). Formulas to extract the effective material constants from solutions for the RVE under three loading cases are derived based on the elasticity theory. An extended rule of mixtures, based on the strength of materials theory for estimating the effective Young’s modulus in the axial direction of the RVE, is applied for comparisons with the numerical solutions based on the elasticity theory. Numerical examples using the FEM are presented, which demonstrate that the load carrying capacities of the CNTs in a matrix are significant. With additions of the CNTs in a matrix at volume fractions of only about 2% and 5%, the stiffness of the composite can increase as many as 0.7 and 9.7 times for the short and long CNT cases, respectively. These simulation results are consistent with the experimental ones reported in the literature.