Hexagonal Representative Volume Element for Modeling and Analysis of Mechanical Properties of Carbon Nanotube Reinforced Composites

Abstract

Carbon nanotubes (CNTs) possess extremely high stiffness, strength and resilience, and may provide the ultimate reinforcing materials for the development of nanocomposites. In this paper, nanostructure is modeled as a linearly elastic composite medium, which consists of a homogeneous matrix having hexagonal representative volume elements (RVEs) and homogeneous cylindrical nanotubes. Formulas to extract the effective material constants from solutions for the RVE under axial as well as lateral loading conditions are derived based on the continuum mechanics approach. Numerical examples using the FEM are presented, which demonstrate that the load carrying capacities of the CNTs in a matrix are significant. For the RVEs having long carbon nanotube, better values of stiffness in axial direction are found as compared to stiffness in the lateral direction. Also, It is found that the square RVEs tend to overestimate the effective Youngs moduli of the CNT-based composites, and the hexagonal RVEs may be the preferred models for obtaining more accurate results.