Journal
COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING
Volume 193, Issue 17-20, Pages 1603-1632Publisher
ELSEVIER SCIENCE SA
DOI: 10.1016/j.cma.2003.12.016
Keywords
multiscale analysis; carbon nanotubes; nanomechanics; virtual atom cluster; meshfree method
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The main objective of this paper is to develop a multiscale method for the analysis of carbon nanotube systems. The multiscale coupled governing equations are first derived based on a multiscale partiton, which consists of a coarse scale component represented by meshfree approximation, and a fine scale component to be resolved from molecular dynamics. It is noted that the coarse scale representation is present in the entire domain of the problem, and coexists with the fine scale representation in the enriched region. Using the projection properties of the partition, the decoupled non-linear set of equations are obtained and solved iteratively using Newton's method. In this multiscale analysis, a virtual atom cluster (VAC) model is also proposed in the coarse scale treatment. This model does not involve a stress update scheme employing the Cauchy-Born hypothesis, which has been widely used in the crystal elasticity theory. Finally. to approximate a curved surface at the nanoscale, meshfree approximations are introduced to interpolate a single layer of atoms. Unlike traditional shell or continuum elements, the geometric constraint is only imposed in two dimensions. The high order continuity property of the meshfree shape functions guarantees an accurate description of the geometry and thus the energy of the atomic bond. The accuracy and efficiency of the method are illustrated in the post-buckling analysis of carbon nanotube structures. To our knowledge, this is the first multiscale post-buckling analysis presented for such a nanoscale system. (C) 2004 Elsevier B.V. All rights reserved.
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