Mechanics of Single- and Multi-Wall Carbon Nanotubes

单壁和多壁碳纳米管的力学性能表现出优异的力学性能，具有极高的刚性和强度。然而，几乎没有对碳纳米管的连续研究，因为人们普遍认为连续力学理论不适用于原子或纳米尺度，必须依赖于原子研究。另一方面，原子学研究在涉及大量碳纳米管的应用中在时间和长度尺度上都有一定的局限性。本工作的目的是发展一个包含碳原子间相互作用势的碳纳米管连续介质理论。我们将采用系统的方法将连续尺度和原子尺度联系起来。通过在原子水平上平均碳键中的键能，得到连续水平上的应变能密度，从而得到碳纳米管的连续本构模型。然后，纳米尺度的连续体将通过原子学研究得到验证。

MECHANICS OF SINGLE- AND MULTI-WALL CARBON NANOTUBESAbstractCarbon nanotubes exhibit superior mechanical properties with extraordinarilyhigh stiffness and strength. There are, however, virtually no continuumstudies of carbon nanotubes because it is generally thought that continuummechanics theories are not applicable on the atomic or nanometer scales, andone must rely on atomistic studies. The atomistic studies, on the otherhand, have some limitations on both the time and length scales forapplications involving a large number of carbon nanotubes.The objective of the work is to develop a continuum theory for carbon nanotubes that incorporates the interatomic potential of carbon. We will adopt a systematic approach to link the continuum and atomistic scales. The strain energy density on the continuum level will be obtained by averaging the bond energy in carbon bonds on the atomic level, which will lead to a continuum constitutive model for carbon nanotubes. The nanoscale continuum will then be validated by the atomistic studies.