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**Application of the higher-order Cauchy-Born rule in mesh-free continuum and multiscale simulation of carbon nanotubes.**
*(English)*
Zbl 1158.74538

Summary: This paper investigates the application of a recently proposed higher-order Cauchy-Born rule in the continuum simulation and multiscale analysis of carbon nanotubes (CNTs). A mesh-free computational framework is developed to implement the numerical computation of the hyper-elastic constitutive model that is derived from the higher-order Cauchy-Born rule. The numerical computation reveals that the buckling pattern of a single-walled carbon nanotube (SWCNT) can be accurately displayed by taking into consideration the second-order deformation gradient, and fewer mesh-free nodes can provide a good simulation of homogeneous deformation. The bridging domain method is employed to couple the developed mesh-free method and the atomistic simulation. The coupling method is used to simulate the bending buckling of an SWCNT and the tensile failure of an SWCNT with a single-atom vacancy defect, and good computational results are obtained.

### MSC:

74S30 | Other numerical methods in solid mechanics (MSC2010) |

74M25 | Micromechanics of solids |

### Keywords:

carbon nanotubes; higher-order Cauchy-Born rule; mesh-free method; continuum simulation; multiscale method; buckling
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\textit{Y. Sun} and \textit{K. M. Liew}, Int. J. Numer. Methods Eng. 75, No. 10, 1238--1258 (2008; Zbl 1158.74538)

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