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Journal of the Mechanics and Physics of Solids 50 (2002) 19411977

Summary: Journal of the Mechanics and Physics of Solids
50 (2002) 1941­1977
An atomistic-based ’nite deformation membrane
for single layer crystalline ’lms
Marino Arroyo1, Ted Belytschko
Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston,
IL 60208-3111, USA
Received 18 August 2001; accepted 11 December 2001
A general methodology to develop hyper-elastic membrane models applicable to crystalline
’lms one-atom thick is presented. In this method, an extension of the Born rule based on the
exponential map is proposed. The exponential map accounts for the fact that the lattice vectors
of the crystal lie along the chords of the curved membrane, and consequently a tangent map
like the standard Born rule is inadequate. In order to obtain practical methods, the exponential
map is locally approximated. The e ectiveness of our approach is demonstrated by numerical
studies of carbon nanotubes. Deformed con’gurations as well as equilibrium energies of atomistic
simulations are compared with those provided by the continuum membrane resulting from this
method discretized by ’nite elements. ? 2002 Elsevier Science Ltd. All rights reserved.
Keywords: A. Buckling; B. Constitutive behavior; B. Shells and membranes; C. Finite elements;


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


Collections: Engineering; Materials Science