Modeling, Simulation, and Analysis of Bending Nanotubes

建议：DMS-0407361PI：John P Wilber研究所：阿克伦大学标题：弯曲纳米管的建模、模拟和分析主要研究人员建议开发多壁碳纳米管的材料模型。该研究将连续介质力学模拟与分子动力学模拟相结合，开发了一种分析弯曲的多尺度程序。在非线性壳理论的框架内建立了连续介质模型。一个新的特征是包含了纳米管壁之间的范德华相互作用。在非局部相互作用的精确形式的各种假设下，研究了所得到的非局部偏微分方程组。然后用对全长多壁纳米管全局几何形状的预测来对局部高应变区进行分子动力学模拟。这些模拟又验证了连续介质模型的本构假设，并用于开发和改进在连续介质水平上包含非局部力的模型。完成后，这项研究产生了准确的多壁碳纳米管的材料模型，以及使用这些模型来分析纳米管对弯曲载荷的响应的技术。这项工作最突出的特点--即建立和分析表示多壁纳米管中壁之间非局部相互作用的方程，以及将连续介质力学模拟与分子动力学模拟相结合--代表了纳米管力学性能研究的重要一步。20世纪90年代初，S发现碳纳米管后，研究人员很快意识到，由于这些材料具有新颖的结构、化学和电学性质，可以用来设计轻质、高强度的复合材料、化学和生化传感器、微电子器件，到目前为止，碳纳米管的实际应用仍然非常有限，因为其机械加工和基本模型的有效技术尚未完全开发出来。虽然在过去的十年中已经收集了大量的实验数据，但很少有人提出能够预测多壁纳米管的力学行为或机械操纵后其物理化学性质的数学模型。特别是，描述多壁碳纳米管弯曲过程的模型很少。提出的研究通过发展描述多壁纳米管弯曲的数学模型和计算技术来解决这一缺陷。这些模型侧重于结合多壁纳米管各壁之间的非局部相互作用的影响。更好地了解纳米管的机械性能和这些管是如何弯曲的，有助于开发制造复合材料和制造含有碳纳米管的纳米器件的技术。除了它的科学影响，拟议的计划还加强了数学、物理和工程学科的研究生和本科生的培训。参与该计划的学生通过宏观数学建模接触到涉及复杂原子的跨学科研究，并接受在多学科环境中工作的培训。

Proposal: DMS-0407361PI: John P WilberInstitution: University of AkronTitle: Modeling, Simulation and Analysis of Bending NanotubesABSTRACTThe 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.