Home

About

Advanced Search

Browse by Discipline

Scientific Societies

E-print Alerts

Add E-prints

E-print Network
FAQHELPSITE MAPCONTACT US


  Advanced Search  

 
Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule M. Arroyo* and T. Belytschko
 

Summary: Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule
M. Arroyo* and T. Belytschko
Department of Mechanical Engineering, Northwestern University, Evanston, Illinois 60208, USA
Received 15 June 2003; revised manuscript received 3 December 2003; published 19 March 2004
A finite deformation continuum theory is derived from interatomic potentials for the analysis of the mechan-
ics 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 involv-
ing severe deformations.
DOI: 10.1103/PhysRevB.69.115415 PACS number s : 81.07.De, 62.25. g, 82.20.Wt
I. INTRODUCTION
Despite the brittle fracture observed in experiments1
and
simulations,2,3
and the development of plasticity predicted by
calculations,4,5

  

Source: Arroyo, Marino - Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya

 

Collections: Engineering; Materials Science