Mechanics of deformation of single- and multi-wall carbon nanotubes

Abstract An effective continuum/finite element (FE) approach for modeling the structure and the deformation of single- and multi-wall carbon nanotubes (CNTs) is presented. Individual tubes are modeled using shell elements, where a specific pairing of elastic properties and mechanical thickness of the tube wall is identified to enable successful modeling with shell theory. The incorporation and role of an initial internal distributed stress through the thickness of the wall, due to the cylindrical nature of the tube, are discussed. The effects of van der Waals forces, crucial in multi-wall nanotubes and in tube/tube or tube/substrate interactions, are simulated by the construction of special interaction elements. The success of this new CNT modeling approach is verified by first comparing simulations of deformation of single-wall nanotubes with molecular dynamics results available in the literature. Simulations of final deformed configurations, as well strain energy histories, are in excellent agreement with the atomistic models for various deformations. The approach was then applied to the bending of multi-wall carbon nanotubes (MWNTs), and the deformed configurations were compared to corresponding high-resolution images from experiments. The proposed approach successfully predicts the experimentally observed wavelengths and shapes of the wrinkles that develop in bent MWNTs, a complex phenomenon dominated by inter-layer interactions. Presented results demonstrate that the proposed FE technique could provide a valuable tool for studying the mechanical behavior of MWNTs as single entities, as well as their effectiveness as load-bearing entities in nanocomposite materials.