In this paper, effects of spatial distribution and geometry of carbon nanotubes (CNTs) on the macroscopic stiffness and microscopic stresses of CNT reinforced polymer composites are investigated based on the multi-scale homogenization theory. An effective fiber model with transversely isotropic constitutive relationship is utilized to describe the nanotube including the surrounding thin matrix layer. Regular and staggered arrays with straight or wavy nanotubes are simulated. The influence of the aspect ratio and volume fraction of CNT, the end gap between two coaxial nanotubes and the distance between two parallel nanotubes on the nanocomposites are also investigated. A new solution method is applied to the homogenization analysis. Numerical results of macroscopic stiffness and microscopic stresses are presented and the influence of various parameters of spatial distribution and geometry of CNTs is discussed in detail.
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