Buckling analysis of carbon nanotubes by a mixed atomistic and continuum model

A mixed atomistic and continuum model is applied to carbon nanotubes, in order to study their buckling behavior. Herein, the term “atomistic” refers to the underlying constitutive model that is formulated on the basis of interatomic potentials, whereas “continuum” means the application of the Cauchy...

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Bibliographic Details
Published in:Computational mechanics 2013-05, Vol.51 (5), p.765-789
Main Authors: Hollerer, Stefan, Celigoj, Christian C.
Format: Article
Language:English
Subjects:
Analysis
Bonding
Buckling
Carbon
Carbon nanotubes
Classical and Continuum Physics
Computational Science and Engineering
Constitutive models
Continuum modeling
Continuums
Deformation
Engineering
Equilibrium equations
Finite element method
Mapping
Mathematical analysis
Mathematical models
Nanotubes
Nonlinear programming
Original Paper
Theoretical and Applied Mechanics
Vectors (mathematics)
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Summary:A mixed atomistic and continuum model is applied to carbon nanotubes, in order to study their buckling behavior. Herein, the term “atomistic” refers to the underlying constitutive model that is formulated on the basis of interatomic potentials, whereas “continuum” means the application of the Cauchy–Born rule, which links the bond vectors before and after deformation via the deformation gradient of the continuum. Because the bond vectors are not infinitesimal and the continuum is modeled as surface, the Cauchy–Born rule has to be appropriately adapted to crystalline sheets. This is done via an exponential mapping in a new and surprisingly simple form such that in the analysis the current configuration has never to be left. The numerical buckling analysis of carbon nanotubes using the mixed atomistic and continuum model is carried out by means of the finite element method. For this purpose, the linearization of the equilibrium equations is provided.
ISSN:0178-7675
1432-0924
DOI:10.1007/s00466-012-0757-z