### Abstract

In this paper, the macroscopic elastic properties of carbon nanotube reinforced composites are evaluated through analysing the elastic deformation of a representative volume element (RVE) under various loading conditions. This RVE contains three components, i.e. a carbon nanotube, a transition layer between the nanotube and polymer matrix and an outer polymer matrix body. First, based on the force field theory of molecular mechanics and computational structural mechanics, an equivalent beam model is constructed to model the carbon nanotube effectively. The explicit relationships between the material properties of the equivalent beam element and the force constants have been set-up. Second, to describe the interaction between the nanotube and the outer polymer matrix at the level of atoms, the molecular mechanics and molecular dynamics computations have been performed to obtain the thickness and material properties of the transition layer. Moreover, an efficient three-dimensional eight-noded brick finite element is employed to model the transition layer and the outer polymer matrix. The macroscopic behaviours of the RVE can then be evaluated through the traditional finite element method. In the numerical simulations, the influences of various important factors, such as the stiffness of transition layer and geometry of RVE, on the final macroscopic material properties of composites have been investigated in detail.

Original language | English |
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Pages (from-to) | 1685-1710 |

Number of pages | 26 |

Journal | Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences |

Volume | 461 |

Issue number | 2058 |

DOIs | |

Publication status | Published - 2005 Jun 8 |

### Keywords

- Carbon nanotube
- Composites
- Elastic property
- Finite element method
- Molecular mechanics
- Representative volume element

### ASJC Scopus subject areas

- Mathematics(all)
- Engineering(all)
- Physics and Astronomy(all)

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## Cite this

*Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences*,

*461*(2058), 1685-1710. https://doi.org/10.1098/rspa.2004.1422