Prediction of the Stiffness and Stresses for Carbon Nano-Tube Composites Based on Homogenization Analysis

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Numerical prediction of the macroscopic stiffness and microscopic stresses for carbon nanotube polymer composites is performed based on the homogenization theory. A new solution method is proposed for the homogenization analysis. The conventional inhomogeneous integral equation related to the microscopic mechanical behavior in the basic unit cell is replaced by a homogeneous integral equation based on a new characteristic function. According to the new solution method, the computational problem of the characteristic function subject to initial strains and periodic boundary conditions is reduced to a simple displacement boundary value problem without initial strains, which simplifies the computational process. The effects of various geometry parameters including straight and wavy nanotubes on the macroscopic stiffness and microscopic stresses are presented. Numerical results are compared with previous results obtained from the Halpin-Tsai equations, Mori-Tanaka method, which proves that the present method is valid and efficient.

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