Atomistic-continuum mechanical models for deformations of single-walled carbon nanotubes
Carbon nanotubes (CNTs) are nanometer sized cylinders made of carbon atoms which possess extraordinary electrical, thermal, and mechanical properties. Their potential applications include such diverse areas as conductive and high strength composites, energy storage and conversion devices, sensors, field emission displays and radiation sources, hydrogen storage media, and nanometer sized semiconductor devices, probes and interconnects. A single-walled carbon nanotube (SWNT) is a CNT formed from a single atomic layer comprised of a hexagonal network of carbon atoms that has been rolled up to form a seamless, hollow cylinder, and it is of interest to understand how the underlying atomic structure determines its macroscopic properties. The present dissertation deals with models to study the influence of atomic structure on the macroscopic mechanical properties of SWNTs. In describing such atomic systems, all-atom simulations using appropriate energetic descriptions are accurate, and often employed. However, these are limited by computational expense to a small number of atoms and time steps. Alternatively, continuum models capture a collective behavior of atoms and are computational efficient. However, the accuracy of traditional continuum models suffers from surface, interface and size effects, and ambiguities in model parameters. Hence, there is a need to develop atomistically enriched continuum models which combine the accuracy of all-atom simulations and the efficiency of continuum analyses. The present dissertation focuses on two zero-temperature, atomistically enriched, large-strain, elastic continuum models to study mechanical deformations of SWNTs - (i) a two-dimensional, quasicontinuum membrane model, and (ii) a one-dimensional rod model. The membrane SWNT model has been employed in prior, published work to predict localized effects such as buckled mode shapes of the effective continuum in severe twist and bending deformations. In the present dissertation, modifications to the existing membrane model are proposed, and implemented in studying coupled extension and twist deformations of SWNTs. The rod model is motivated by the need to model global behavior of long SWNTs in which the aforementioned localized effects are not of significant interest. It is a unified, large-strain SWNT model capable of simultaneously accounting for (a) bending, (b) twist, (c) shear, (d) extension, (e) coupled extension and twist, and (f) coupled bending and shear deformation modes. Both the atomistic-continuum SWNT models in the present dissertation demonstrate the benefits of accounting for important anisotropic and large-strain effects as improvements over employing traditional, linearly elastic, isotropic, small-strain, continuum models. It is envisioned that the ideas presented in this dissertation can be extended to other atomic systems such as silicon or boron nitride nanotubes by use of appropriate lattices and energetic descriptions.
single-walled carbon nanotubes (SWNTs); constitutive behavior; hyperelastic material; finite deformations; finite strains; atomistic-continuum model; membrane; rod; quasicontinuum
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