Circumferential Nonlocal Effect On The Mechanical Behavior Of Carbon Nanotubes And Their Changes With The Curvatures

With the rapid development of nano science and technology, more and more advanced nano materials are known to the people. As one of the outstanding representatives of advanced nano materials, carbon nanotubes (CNTs) have been studied by researchers because of their high strength and stiffness. Nonlocal constitutive relation is an important embodiment of the new physical properties of nano materials (i.e. small scale effect), which leads to the unique mechanical behavior and properties of nano materials. The nonlocal effect (constitutive relation) of cylindrical carbon nanotubes (CNTs) is derived from the axial and circumferential strain gradients((?)2u/(?)x2, (?)2w/(?)θ2). However, the mechanical behavior of carbon nanotubes are widely used for the characterization of nonlocal beam theory which can characterize axial nonlocal effects, circumferential nonlocal effect (CNE) was completely ignored in the one-dimensional theoretical model. Therefore circumferential nonlocal effect of carbon tube mechanical properties become the key of evaluation of nonlocal beam theory, the reliability and the scope of its application. On the other hand, carbon nanotubes with nonlocal constitutive issues of common concern value of nonlocal constant e0a in the relationship and scholars, and in the literature of different research results in larger dispersion. Therefore, carbon nanotubes obtained reliable e0a value and e0a value of the previous big dispersion put forward a reasonable explanation, has become the main contents of the research on the local mechanical problem of non carbon nanotubes. Based on the above reasons, the single wall carbon nanotubes (SWCNTs) are selected as a typical example to address the issues,which are consisted by two components.(1) The qualitative assessment of CNE on buckling and transverse free vibration of SWCNTs. The nonlocal shell model considering axial and CNE and nonlocal beam model only considering axial nonlocal effect are used to calculate the carbon nanotube axial buckling critical value and free vibration frequency and the difference of two models to evaluate CNE on buckling and vibration of SWCNTs. The results show that the CNE is substantial for the buckling and transverse free vibration of the CNTs with small radius, if the nonlocal coefficient is taken as 0.21 nm,the critical buckling strain of axially compressed buckling of thin SWCNTs of a radius r<1 nm is decreased by up to 45%,and the frequency is decreased by up to 21%. But the CNE on SWCNTs of a radius r>2.38 nm for the buckling and transverse free vibration is small and can be neglected.(2) The radius-dependence of the coefficient (eoa)c of CNE is calculated for the SWCNTs. By means of molecular dynamics simulation (MDs) of the buckling of CNTs with different radius, the CNE parameters of carbon nanotubes with different curvature radius were obtained. And then the radius-dependence of the coefficient of CNE is exammined by fitting the nonlocal shell model. The results show that:the parameter of CNE is proportional to the curvature radius.With the increase of the radius, the parameter of CNE is gradually increasing, and the ratio is constant 1.1.It is noted that the research work of part (1) is under the premise of that the parameter of nonlocal effcet is 0.21nm, but the parameters of CNE are increased in proportion with the increasing of curvature radius,which makes the scopes of influence the CNE grow accordingly. Therefore, it is necessary to modify the influence scopes of the CNE in part (1). Hence, the part (2) of the research work is actually the development and revision of the research work in part (1).It further defines the influence of CNE on the mechanical behavior of CNTs in quantity.