Application of homogenization method on the evaluation and analysis of the effective stiffness for noncontinuous carbon nanotube/polymer composites

The effective stiffness of noncontinuous carbon nanotubes (CNTs)/polymer composites are predicted by the homogenization method with exact periodic boundary conditions. Numerical calculations for regular and staggered array models are performed by the macro-microscopic finite element methods. The results are compared with those from Mori-Tanaka and Halpin-Tsai theories, which show that the stiffness of CNTs composites are not only related to aspect ratio and CNTs volume fraction as described in the earlier theories, but also sensitive to the space between CNTs ends, the distribution of CNTs within the selected representative volume element, and the geometrical shape of CNTs. The results from the two empirical approaches are included in the present results with special spacing ratios of horizontal and vertical fiber ends (T _f/H_f). It is proved that the homogenization method is an efficient method to predict the effective stiffness of CNTs/polvmer composites with periodic microstructure.