TY - JOUR
T1 - Explicit expressions of mechanical properties for graphene sheets and carbon nanotubes via a molecular-continuum model
AU - Hwu, Chyanbin
AU - Yeh, Yu Kuei
N1 - Funding Information:
The authors would like to thank National Science Council, Taiwan, R.O.C. for support through Grants NSC 97-2923-E-006-001-MY3.
PY - 2014/4
Y1 - 2014/4
N2 - Through the equivalence of potential energy and elastic strain energy, a molecular-continuum model combining the concepts of molecular dynamics and continuum mechanics is proposed. Unlike the usual test performed by applying forces, in this model a uniform strain field is employed in the representative volume element of specimens. Through this model, the Young's moduli, Poisson's ratios, and shear modulus of graphene sheets and carbon nanotubes (armchair, zigzag, or chiral) can all be written as a simple rational function in which the dependence of radius, chiral angle and thickness can be observed clearly from the explicit closed-form expression. Moreover, according to the proposed molecular-continuum model, an integrated symbolic and numerical computational scheme (ISNC) is established to deal with the general nanoscale elastic solids. Identical results of the closed-form solutions and ISNC verify the correctness of our derivation. Comparison with the results obtained by the other methods or by different potential energy function further justifies the simplicity, validity and efficiency of the proposed model.
AB - Through the equivalence of potential energy and elastic strain energy, a molecular-continuum model combining the concepts of molecular dynamics and continuum mechanics is proposed. Unlike the usual test performed by applying forces, in this model a uniform strain field is employed in the representative volume element of specimens. Through this model, the Young's moduli, Poisson's ratios, and shear modulus of graphene sheets and carbon nanotubes (armchair, zigzag, or chiral) can all be written as a simple rational function in which the dependence of radius, chiral angle and thickness can be observed clearly from the explicit closed-form expression. Moreover, according to the proposed molecular-continuum model, an integrated symbolic and numerical computational scheme (ISNC) is established to deal with the general nanoscale elastic solids. Identical results of the closed-form solutions and ISNC verify the correctness of our derivation. Comparison with the results obtained by the other methods or by different potential energy function further justifies the simplicity, validity and efficiency of the proposed model.
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U2 - 10.1007/s00339-014-8241-6
DO - 10.1007/s00339-014-8241-6
M3 - Article
AN - SCOPUS:84903279873
SN - 0947-8396
VL - 116
SP - 125
EP - 140
JO - Applied Physics A: Materials Science and Processing
JF - Applied Physics A: Materials Science and Processing
IS - 1
ER -