Continuum Modelling of Carbon Nanotube Composites: A Review

Carbon nanotubes (CNTs) have been proven to show exceptional mechanical properties such as longitudinal elastic modulus of up to 1TPa and elastic strain of around 5%. Possessing these excellent properties, while having a fibre-like structure, CNTs have considerable potential to act as fillers in highly strong and light CNT composite (CNTC) materials. However, from experiments conducted, the biggest challenge before these nanocomposites can become a reality is that they do not show the expected excellent properties. This has led to extensive research into determining the effective properties of the CNTC using the preferred method of fully or semi-continuum modelling through the application of the finite element method (FEM). In this paper a review on aspects of the continuum representation of CNTCs is conducted. It covers the development, analysis and results of partial or full continuum modelling conducted in the last decades. A close-to-reality model must consider at least 5 CNT characteristics: length, interphase, waviness, orientation and agglomeration that cover 4 scales from nanoscale through micro- and meso- to macro-scale. The earlier nanocomposite continuum representatives mostly consisted of a CNT fibre surrounded by a matrix that could only catch the CNT characteristics at nano- and micro-scales and thus provided nanocomposite properties that were close to the rule of mixture (ROM) values but very far from experimental values. However, the recent representations manage to reach macro-scale level while representing important CNT characteristics such that the results were found to be close to the experimental results.