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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Int. J. Numer. Meth. Engng 2004; 59:419456 (DOI: 10.1002/nme.944)
 

Summary: INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
Int. J. Numer. Meth. Engng 2004; 59:419­456 (DOI: 10.1002/nme.944)
Finite element methods for the non-linear mechanics of
crystalline sheets and nanotubes
M. Arroyo
and T. Belytschko;
Department of Mechanical Engineering; Northwestern University; Evanston; IL 60208; U.S.A.
SUMMARY
The formulation and ’nite element implementation of a ’nite deformation continuum theory for the
mechanics of crystalline sheets is described. This theory generalizes standard crystal elasticity to curved
monolayer lattices by means of the exponential Cauchy­Born rule. The constitutive model for a two-
dimensional continuum deforming in three dimensions (a surface) is written explicitly in terms of the
underlying atomistic model. The resulting hyper-elastic potential depends on the stretch and the curva-
ture of the surface, as well as on internal elastic variables describing the rearrangements of the crystal
within the unit cell. Coarse grained calculations of carbon nanotubes (CNTs) are performed by discretiz-
ing this continuum mechanics theory by ’nite elements. A smooth discrete representation of the surface
is required, and subdivision ’nite elements, proposed for thin-shell analysis, are used. A detailed set of
numerical experiments, in which the continuum/’nite element solutions are compared to the correspond-
ing full atomistic calculations of CNTs, involving very large deformations and geometric instabilities,
demonstrates the accuracy of the proposed approach. Simulations for large multi-million systems illus-

  

Source: Arroyo, Marino - Departament de Matemątica Aplicada III, Universitat Politčcnica de Catalunya

 

Collections: Engineering; Materials Science