Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule

被引:349
作者
Arroyo, M [1 ]
Belytschko, T [1 ]
机构
[1] Northwestern Univ, Dept Mech Engn, Evanston, IL 60208 USA
来源
PHYSICAL REVIEW B | 2004年 / 69卷 / 11期
关键词
D O I
10.1103/PhysRevB.69.115415
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
A finite deformation continuum theory is derived from interatomic potentials for the analysis of the mechanics of carbon nanotubes. This nonlinear elastic theory is based on an extension of the Cauchy-Born rule called the exponential Cauchy-Born rule. The continuum object replacing the graphene sheet is a surface without thickness. The method systematically addresses both the characterization of the small strain elasticity of nanotubes and the simulation at large strains. Elastic moduli are explicitly expressed in terms of the functional form of the interatomic potential. The expression for the flexural stiffness of graphene sheets, which cannot be obtained from standard crystal elasticity, is derived. We also show that simulations with the continuum model combined with the finite element method agree very well with zero temperature atomistic calculations involving severe deformations.
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页数:11
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