Modeling, Simulation, and Analysis of Bending Nanotubes

项目申请：DMS-0407361PI: John P WilberInstitution: University of akron题目：弯曲纳米管的建模、仿真与分析摘要主要研究人员提出建立多壁碳纳米管的材料模型。该研究将连续力学建模与分子动力学模拟相结合，开发了一种多尺度的弯曲分析方法。在非线性壳理论的框架内建立了连续体模型。一个新颖的特征是纳米管壁之间包含了范德华相互作用。在对非局部相互作用精确形式的各种假设下，研究了得到的非局部偏微分方程组。对全长多壁纳米管的整体几何形状的预测，然后用于局部高应变区域的分子动力学模拟。反过来，模拟验证了连续体模型的本构假设，并用于开发和完善模型，以便在连续体水平上包含非局部力。在此基础上，本研究获得了精确的多壁碳纳米管材料模型，并利用这些模型分析了纳米管在弯曲载荷作用下的响应。该研究最显著的特点是，对多壁纳米管中壁间非局部相互作用的方程进行了表述和分析，并将连续介质力学建模与分子动力学模拟相结合，这是研究纳米管力学性能的重要一步。在20世纪90年代初发现碳纳米管后不久，研究人员就意识到，由于这些材料具有新颖的结构、化学和电学性质，可以用于设计轻质、高强度的复合材料、化学和生化传感器、微电子器件等。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础模型的有效技术尚未完全开发。虽然在过去的十年中收集了大量的实验数据，但很少有数学模型能够预测多壁纳米管的力学行为或机械操作后的物理化学性质。特别是，很少有模型可以描述多壁碳纳米管的弯曲过程。提出的研究通过开发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点。这些模型的重点是纳入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以及这些管如何弯曲有助于生产复合材料和制造包含碳纳米管的纳米级器件的技术的发展。除了它的科学影响，拟议的计划加强研究生和本科生在数学，物理和工程学科的训练。参与该计划的学生将接触到跨学科的研究，包括通过宏观数学建模的复杂原子，并在多学科环境中进行工作培训。

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.