Effect of the Periodic Distributions of Carbon Nanotube on Homogenized Effective Stiffness for Nanotube Reinforced Polymer Composites

By means of the virtual work theory and asymptotic expansion homogenization method (HM) with rigorous mathematically multi-scale perturbation theory, an improved homogeneous integral equation with simple and precise periodic boundary conditions is obtained to predict the homogenized effective stiffness of carbon nanotubes (CNTs) reinforced composites. Two and three dimensional CNTs-composites are analyzed by the proposed model. The present results with special ratio between longitudinal and transverse intervals for nanotubes (T f /H f ) are compared well with those from empirical Halpin-Tsai and Mori-Tanaka approaches, which indicate that the present analysis has a relatively wide range to consider the effects of CNTs distribution on macroscopic mechanical properties of CNTs-composites. The results show that it is possible to design composites with high stiffness by considering a reasonable ratio between longitudinal and transverse intervals for discontinuous carbon nanotubes.