A finite element study on the effect of curvature on the reinforcement of matrices by randomly distributed and curved nanotubes

A significant reinforcement effect has always been expected from the use of carbon nanotubes (CNT). Well-known experimental results, however, reveal that the theoretical reinforcement rules for straight nanotubes are not always achieved in practice. This paper reports that not only should the percentage quantity of nanotubes in the matrix be taken into account, but also their curvatures. A finite element method (FEM) based computational analysis on the mechanical reinforcement of composite materials by nanotubes is presented. In this article we focus on randomly distributed and curved nanotubes as fillers. In particular, we study the influence of the curvature of the nanotubes on the overall elastic moduli. To this end, we apply a statistical analysis of the elastic moduli of nanocomposites when a certain number of nanotubes are incorporated into a matrix. Here, we restrict ourselves to use just a simple as possible linear elasticity model. Nevertheless, it turns out that the average overall reinforcement ratio is significantly lower than in the case of aligned straight nanotubes. In particular, our numerical experiments show that the resulting reinforcement ratios exhibit a linear dependency on the average ratio of the end-to-end distance and the length of the nanotube.