Multi-scale Simulation On Compression Buckling Behavior Of Branched Carbon Nanotubes

Branched carbon nanotubes have attracted much attention from more and morescientists and scholars in further studying due to their symmetrical structures andamazing electronic properties. However, it’s very difficult to conduct the experiment onbranched carbon nanotubes owing to the size and structures. Therefore, the numericalsimulation methods have been applied to predict mechanical behaviors of branchedcarbon nanotubes. In this paper, the atomic-scale finite element method (AFEM) basedon the “second generation” empirical potential of Tersoff-Brenner and the traditionalcontinuum finite element method (FEM) are adopted to simulate the dynamic bucklingbehavior of the single-walled straight carbon nanotubes (SWCNTs) and branchedcarbon nanotubes (BSWCNTs) under axial compression. The effects of the length, theradius and the chirality of carbon nanotubes on the compression buckling behavior arediscussed. The following conclusions can be drawn from the present study:(1) First of all, the atomic-scale finite element method and the continuum finiteelement method are used to simulate the dynamic buckling behavior of the SWCNTsunder axial compression. The dynamic buckling behavior of the SWCNTs with thelength of6nm and the chirality of (3,3) to (10,10)(corresponding to the radius of0.2nm-0.7nm) is simulated, and it is found that the critical buckling load of SWCNTs firstincreases to reach a maximum at chirality (8,8)(i.e., the radius is about0.5nm), andthen decreases with increasing the radius. The dynamic buckling behavior of SWCNTswith the chirality (5,5) and the length of2nm to10nm is simulated, which shows thatthe critical buckling load of SWCNTs decreases gradually with increasing the length.When the length is less than6nm, the local buckling modes are mainly presented.When the length is more than6nm, the SWCNTs are more prone to the global bucklingmodes. It also shows that the longer the length, the required critical buckling stress ofthe structure is the smaller. In this paper, our simulation results have a good agreementwith the result of other researchers using the molecular dynamic method (MD), whichindicates that AFEM and FEM are reliable in simulating the dynamic buckling behaviorof carbon nanotubes.(2) Secondly, the atomic-scale finite element method and the continuum finite element method are adopted to simulate the dynamic buckling behavior of “Y”-shapedBSWCNTs under axial compression. The dynamic buckling behavior of BSWCNTswith the branched length of2nm and the chirality (3,3) to (10,10) is simulated, theresults show that the critical buckling load first increases to reach the peak at chirality (5,5)(i.e., the radius is about0.34nm), and then decreases with increasing the radius.When the radius is larger than0.4nm, the fracture of partial atomic bonds in branchedjunction makes the buckling load decline obviously. At the same time, the dynamicbuckling behavior of the BSWCNTs with chirality (5,5) and branched length rangingfrom1nm to4nm is simulated, and it is found that the critical buckling load graduallydecreases with increasing the length, implying that the length is larger, the structure ismore unstable. In addition, compared axial buckling behavior of three different chiral (5,5)(6,4)(8,0) BSWCNTs, armchair typed structures tend to be more stable than thezigzag typed for the same radius and length.(3) Finally, compared the simulation results of the AFEM and FEM for theBSWCNTs with the branched length of1nm to4nm, these two numerical results showa good agreement within the radius is less than0.4nm, which illustrates that the FEMcan be used to predict dynamic buckling properties of the BSWCNTs in a certain extent.