NER: Mathematical Modeling of the Constitutive Response of Carbon Nanotubes

碳纳米管本构响应的数学建模主要研究人员：Hamid Bellout和Frederick Bloom北伊利诺伊大学数学科学系DeKalb，IL 60115这项建议是对纳米和工程倡议NSF03-043，类别的响应在原子尺度上使用分子动力学模拟，主要研究人员构建了石墨片本构行为的数学模型；这是通过将均化理论应用于具有特定手性矢量的碳原子的六角形阵列来实现的。分子动力学模拟为石墨片生成了一组周期性的、快速变化的弹性常数，其中包含了以前被忽略的应变的扭转分量。然后将分析扩展到相同手性的单壁纳米管表面上的特定碳原子阵列，目的是确定将石墨片模拟为连续统到纳米管表面的变形。所导出的单壁纳米管的有效本构关系允许计算纳米管壳的有效厚度，并将建模工作扩展到多壁纳米管。特别是，这项研究导致了关于单壁和多壁碳纳米管压缩屈曲的新结果，并对其在纳米管复合材料中的极限强度进行了预测；它还消除了对昂贵且耗时的分子动力学研究的需要。由于纳米结构非金属材料具有显著改善传统结构材料的力学和物理性能的潜力，因此引起了人们对纳米结构非金属材料的广泛兴趣。尤其是碳纳米管，被认为具有任何其他已知材料无法比拟的强度，基于碳纳米管的复合材料具有提供超过现有任何材料的强度与重量比的潜力。由于小纤维复合材料相对容易加工，碳纳米管的力学性能使其成为制备最佳碳纤维增强材料的杰出候选者。目前的研究工作致力于发展预测单个纳米管的力学性能的理论；这种知识是根据聚合物的分子结构、纳米管和聚合物/纳米管界面来理解纳米管-聚合物复合材料的整体力学性能的先决条件。纳米管增强聚合物复合材料已经被认为是未来理想的结构材料，其应用范围从用于下一代民用、军用和航天器和飞机的先进部件，到武装部队成员的防护服。

Mathematical Modeling of the Constitutive Response of Carbon NanotubesPrincipal Investigators: Hamid Bellout and Frederick BloomDepartment of Mathematical SciencesNorthern Illinois UniversityDeKalb, IL 60115 This proposal was received in response to Nanoscale and Engineering Initiative NSF 03-043, Category NER Using molecular dynamics simulations at the atomic scale, the principal investigators construct a mathematical model for the constitutive behavior of a graphitic sheet; this is accomplished by applying homogenization theory to a hexagonal array of carbon atoms with a specific chirality vector. The molecular dynamics simulations generate a set of periodic, rapidly varying, elastic constants for the graphitic sheet which incorporate the previously ignored torsional component of strain. The analysis is then extended to specific arrays of carbon atoms on the surface of a single-walled nanotube of the same chirality with the goal of determining the deformation which takes the graphitic sheet, modeled as a continuum, onto the nanotube surface. The derived effective constitutive relations for single-walled nanotubes allows for the computation of an effective thickness for nanotube shells and for an extension of the modeling effort to multiwalled nanotubes. In particular, the research leads to new results concerning the compressive buckling of single-walled and multi-walled carbon nanotubes and predictions of their ultimate strength in nanotube composites; it also obviates the need for an expanding array of expensive and time-consuming molecular dynamics studies.Considerable interest has been generated in nano-structured non-metallic materials because of their potential for providing significant improvements in both mechanical and physical properties with respect to traditional structural materials. Carbon nanotubes, in particular, are believed to possess a strength which is unmatched by any other known material and composite materials based on carbon nanotubes have the potential of providing strength-to-weight ratios exceeding those of any materials currently available. Because small fiber composites are relatively easy to process, the mechanical properties of carbon nanotubes make them outstanding candidates for the fabrication of the optimal carbon fiber reinforced materials. The present research effort is geared towards the development of theories for predicting the mechanical properties of individual nanotubes; such knowledge is a prerequisite for understanding the bulk mechanical properties of nanotube-polymer composites in terms of the molecular structure of the polymer, the nanotubes, and the polymer/nanotube interfaces. Nanotube reinforced polymer composites are already being thought of as the ideal structural materials of the future for applications which range from advanced components for the next generation of civilian, military, and space vehicles and aircraft to protective uniforms for members of the armed forces.