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

• Published in: Applied physics. A, Materials science & processing Materials science & processing, 2009-06, Vol.95 (3), p.819-831
• Main Authors: Fan, C. W., Liu, Y. Y., Hwu, Chyanbin
• Format: Article
• Language: English
• Subjects: Characterization and Evaluation of Materials; Computer simulation; Condensed Matter Physics; Condensed matter: structure, mechanical and thermal properties; Estimating; Exact sciences and technology; Finite element method; Interlayers; Machines; Manufacturing; Mathematical analysis; Mathematical models; Mechanical and acoustical properties of condensed matter; Mechanical properties; Mechanical properties of nanoscale materials; Nanotechnology; Optical and Electronic Materials; Physics; Physics and Astronomy; Processes; Surfaces and Interfaces; Thin Films; Van der Waals forces
• ISSN: 0947-8396; 1432-0630
• DOI: 10.1007/s00339-009-5080-y

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.