0

Full Content is available to subscribers

Subscribe/Learn More  >

A New Hierarchical Technique for the Multiscale Modeling of Carbon Nanostructures

[+] Author Affiliations
Arash Mahdavi, Eric Mockensturm

Pennsylvania State University

Paper No. IMECE2005-82988, pp. 597-600; 4 pages
doi:10.1115/IMECE2005-82988
From:
  • ASME 2005 International Mechanical Engineering Congress and Exposition
  • Microelectromechanical Systems
  • Orlando, Florida, USA, November 5 – 11, 2005
  • Conference Sponsors: Microelectromechanical Systems Division
  • ISBN: 0-7918-4224-X | eISBN: 0-7918-3769-6
  • Copyright © 2005 by ASME

abstract

We present a new hierarchical modeling technique called the Consistent Atomic-scale Finite Element (CAFÉ) method [1]. Unlike traditional approaches for linking the atomic structure to its equivalent continuum [2-7], this method directly connects the atomic degrees of freedom to a reduced set of finite element degrees of freedom without passing through an intermediate homogenized continuum. As a result, there is no need to introduce stress and strain measures at the atomic level. This technique partitions atoms to masters and salves and reduces the total number of degrees of freedom by establishing kinematic constraints between them [5-6]. The Tersoff-Brenner interatomic potential [8] is used to calculate the consistent tangent stiffness matrix of the structure. In this finite element formulation, all local and non-local interactions between carbon atoms are taken into account using overlapping finite elements (Figure 1b). In addition, a consistent hierarchical finite element modeling technique is developed for adaptively coarsening and refining the mesh over different parts of the model (Figure 2a, 2b). The stiffness of higher-rank elements is approximated using the stiffness of lower-rank elements and kinematic constraints. This process is consistent with the underlying atomic structure and, by refining the mesh, molecular dynamic results will be recovered. This method is valid across the scales and can be used to concurrently model atomistic and continuum phenomena so, in contrast with most other multiscale methods [4-7], there is no need to introduce artificial boundaries for coupling atomistic and continuum regions. Effect of the length scale of the nanostructure is also included in the model by building the hierarchy of elements from bottom up using a finite size atom cluster as the building block (Figures 2a, 2b). In this method by introducing two independent field variables, the so-called inner displacement is taken into account (Fig. 3b). Applicability of the method is shown with several examples of deformation of carbon nanostructures such as graphene sheet, nanotube, and nanocone, subjected to different loads and boundary conditions.

Copyright © 2005 by ASME

Figures

Tables

Interactive Graphics

Video

Country-Specific Mortality and Growth Failure in Infancy and Yound Children and Association With Material Stature

Use interactive graphics and maps to view and sort country-specific infant and early dhildhood mortality and growth failure data and their association with maternal

NOTE:
Citing articles are presented as examples only. In non-demo SCM6 implementation, integration with CrossRef’s "Cited By" API will populate this tab (http://www.crossref.org/citedby.html).

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In