Modeling, Simulation, and Analysis of Bending Nanotubes

University Of Akron, Akron OH

Investigators

Abstract

Proposal: DMS-0407361 PI: John P Wilber Institution: University of Akron Title: Modeling, Simulation and Analysis of Bending Nanotubes ABSTRACT The principal investigators propose to develop material models of multi-walled carbon nanotubes. The research combines continuum mechanical modeling with molecular dynamics simulations to develop a multiscale procedure for analyzing bending. The continuum models are formulated within the framework of nonlinear shell theory. A novel feature is the inclusion of van der Waals interactions between the walls of the nanotube. The resulting systems of nonlocal partial differential equations are studied under various assumptions on the precise form of the nonlocal interactions. The predictions for the global geometry of full-length multi-walled nanotubes are then used to conduct molecular dynamics simulations of the localized high-strain regions. The simulations, in turn, verify the constitutive assumptions of the continuum model and are used to develop and refine the models for the inclusion of the non-local forces at the continuum level. Upon its completion, this research yields accurate material models of multi-walled carbon nanotubes and techniques for using these models to analyze the response of nanotubes to applied bending loads. The mostsalient features of the proposed work---namely, the formulation and analysis of equations with terms representing the nonlocal interactions between walls in multi-walled nanotubes and the integration of continuum mechanical modeling with molecular dynamics simulations---represent a significant step in the study of the mechanical properties of nanotubes.Soon after the discovery of carbon nanotubes in the early 1990's, researchers realized that these materials, because of their novel structural, chemical, and electrical properties, could be used to engineer light-weight, high-strength composite materials, chemical andbiochemical sensors, micro-electronic devices, etc. So far the practical uses of carbon nanotubes remain very limited because the efficient technologies for their mechanical processing and underlying models have not yet been fully developed. Although a great deal ofexperimental data has been collected during the past decade, few mathematical models have been suggested that can predict either the mechanical behavior of multi-walled nanotubes or their physical-chemical properties after mechanical manipulation. In particular, few models exist to describe the process of bending of multi-walled carbon nanotubes. The proposed research addresses this shortcoming by developing mathematical models and computationaltechniques for describing the bending of multi-walled nanotubes. These models focus on incorporating the effect of nonlocal interactions between the individual walls of a multi-walled nanotube. A better understanding of the mechanical properties of nanotubes andof how these tubes bend contributes to the development of techniques for producing composite materials and for manufacturing nano-scale devices incorporating carbon nanotubes. In addition to its scientific impact, the proposed program enhances graduate and undergraduatetraining in the disciplines of mathematics, physics, and engineering. The students participating in the program are exposed to interdisciplinary research involving sophisticated atomic through macroscopic mathematical modeling and are trained in working within a multi-disciplinary environment.