Comparison of analytical and numerical methods for homogenization of nanotube-reinforced polymers

Carbon nanotubes are increasingly getting impact as reinforcing material for polymer based nanocomposites. Hence, new modeling strategies are necessary to calculate the behavior of these materials. In the last years some attempts have been made using and developing classical micromechanical models. On the other hand numerical homogenization methods are available to tackle this problem. Examples for both types of modeling strategies are presented with focus on the nanotube geometry. The nanotubes are modeled as hollow tubes as well as as isotropic and transversely isotropic cylinders. As expected the results of numerical and analytical methods are identical for isotropic cylinder inclusions. Small deviations occur for transversely isotropic cylinders in transverse direction. In the case of hollow tube inclusions, the analytical models lead to lower stiffness values in transverse direction and for shear. The largest deviations occur for longitudinal shear with magnitudes smaller than 10%. In contrast the effort to get numerical results is enormous, so that the analytical models are still useful. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)