Summary: DOI 10.1007/s11012-005-2133-y
Meccanica (2005) 40: 455­469 © Springer 2005
Continuum Mechanics Modeling and Simulation of Carbon
Nanotubes
MARINO ARROYO1,
and TED BELYTSCHKO2
1
Departament de Matem`atica Aplicada III, Laboratori de C`alcul Num`eric (LaCaN), Universitat
Polit`ecnica de Catalunya, E-08034 Barcelona, Spain
2
Department of Mechanical Engineering, Northwestern University, Evanston, IL 60208, USA
(Accepted: 27 July 2005)
Abstract. The understanding of the mechanics of atomistic systems greatly benefits from continuum
mechanics. One appealing approach aims at deductively constructing continuum theories starting from
models of the interatomic interactions. This viewpoint has become extremely popular with the quas-
icontinuum method. The application of these ideas to carbon nanotubes presents a peculiarity with
respect to usual crystalline materials: their structure relies on a two-dimensional curved lattice. This
renders the cornerstone of crystal elasticity, the Cauchy­Born rule, insufficient to describe the effect of
curvature. We discuss the application of a theory which corrects this deficiency to the mechanics of car-
bon nanotubes (CNTs). We review recent developments of this theory, which include the study of the

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

Collections: Engineering; Materials Science