### Abstract

A finite element simulation technique for estimating the mechanical properties of multi-walled carbon nanotubes is developed. In the present modeling concept, individual carbon nanotube is simulated as a frame-like structure and the primary bonds between two nearest-neighboring atoms are treated as beam elements, the beam element properties are determined via the concept of energy equivalence between molecular dynamics and structural mechanics. As to the simulation of the interlayer van der Waals force which has intrinsic nonlinearity and complicated applying region, a simplifying method is proposed that the interlayer pressure caused by van der Waals force instead of the force itself is to be considered, and we make use of the linear part of the interlayer pressure near the equilibrium condition to avoid the nonlinearity in problem, then linear spring elements whose stiffness is determined by equivalent force concept can be utilized to simulate the interlayer van der Waals force such that significant modeling and computing effort is saved in performing the finite element analysis. Numerical examples for estimating the mechanical properties of nanotubes, such as axial and radial Young's modulus, shear modulus, natural frequency, buckling load, etc., are presented to illustrate the accuracy of this simulation technique. By comparing to the results found in the literature and the possible analytical solutions, it shows that the obtained mechanical properties of nanotubes by the present method agree well with their comparable results. In addition, the relations between these mechanical properties and the nanotube size are also discussed.

Original language | English |
---|---|

Pages (from-to) | 819-831 |

Number of pages | 13 |

Journal | Applied Physics A: Materials Science and Processing |

Volume | 95 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2009 Jun 1 |

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### All Science Journal Classification (ASJC) codes

- Chemistry(all)
- Materials Science(all)

### Cite this

*Applied Physics A: Materials Science and Processing*,

*95*(3), 819-831. https://doi.org/10.1007/s00339-009-5080-y

}

*Applied Physics A: Materials Science and Processing*, vol. 95, no. 3, pp. 819-831. https://doi.org/10.1007/s00339-009-5080-y

**Finite element simulation for estimating the mechanical properties of multi-walled carbon nanotubes.** / Fan, C. W.; Liu, Y. Y.; Hwu, Chyanbin.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Finite element simulation for estimating the mechanical properties of multi-walled carbon nanotubes

AU - Fan, C. W.

AU - Liu, Y. Y.

AU - Hwu, Chyanbin

PY - 2009/6/1

Y1 - 2009/6/1

N2 - A finite element simulation technique for estimating the mechanical properties of multi-walled carbon nanotubes is developed. In the present modeling concept, individual carbon nanotube is simulated as a frame-like structure and the primary bonds between two nearest-neighboring atoms are treated as beam elements, the beam element properties are determined via the concept of energy equivalence between molecular dynamics and structural mechanics. As to the simulation of the interlayer van der Waals force which has intrinsic nonlinearity and complicated applying region, a simplifying method is proposed that the interlayer pressure caused by van der Waals force instead of the force itself is to be considered, and we make use of the linear part of the interlayer pressure near the equilibrium condition to avoid the nonlinearity in problem, then linear spring elements whose stiffness is determined by equivalent force concept can be utilized to simulate the interlayer van der Waals force such that significant modeling and computing effort is saved in performing the finite element analysis. Numerical examples for estimating the mechanical properties of nanotubes, such as axial and radial Young's modulus, shear modulus, natural frequency, buckling load, etc., are presented to illustrate the accuracy of this simulation technique. By comparing to the results found in the literature and the possible analytical solutions, it shows that the obtained mechanical properties of nanotubes by the present method agree well with their comparable results. In addition, the relations between these mechanical properties and the nanotube size are also discussed.

AB - A finite element simulation technique for estimating the mechanical properties of multi-walled carbon nanotubes is developed. In the present modeling concept, individual carbon nanotube is simulated as a frame-like structure and the primary bonds between two nearest-neighboring atoms are treated as beam elements, the beam element properties are determined via the concept of energy equivalence between molecular dynamics and structural mechanics. As to the simulation of the interlayer van der Waals force which has intrinsic nonlinearity and complicated applying region, a simplifying method is proposed that the interlayer pressure caused by van der Waals force instead of the force itself is to be considered, and we make use of the linear part of the interlayer pressure near the equilibrium condition to avoid the nonlinearity in problem, then linear spring elements whose stiffness is determined by equivalent force concept can be utilized to simulate the interlayer van der Waals force such that significant modeling and computing effort is saved in performing the finite element analysis. Numerical examples for estimating the mechanical properties of nanotubes, such as axial and radial Young's modulus, shear modulus, natural frequency, buckling load, etc., are presented to illustrate the accuracy of this simulation technique. By comparing to the results found in the literature and the possible analytical solutions, it shows that the obtained mechanical properties of nanotubes by the present method agree well with their comparable results. In addition, the relations between these mechanical properties and the nanotube size are also discussed.

UR - http://www.scopus.com/inward/record.url?scp=63949087028&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=63949087028&partnerID=8YFLogxK

U2 - 10.1007/s00339-009-5080-y

DO - 10.1007/s00339-009-5080-y

M3 - Article

AN - SCOPUS:63949087028

VL - 95

SP - 819

EP - 831

JO - Applied Physics

JF - Applied Physics

SN - 0340-3793

IS - 3

ER -