A new hierarchical technique for the multiscale modeling of carbon nanostructures

Arash Mahdavi, Eric M. Mockensturm

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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.

Original languageEnglish (US)
Title of host publicationAmerican Society of Mechanical Engineers, Micro-Electro Mechanical Systems Division, (Publications) MEMS
Pages597-600
Number of pages4
DOIs
StatePublished - Dec 1 2005
Event2005 ASME International Mecahnical Engineering Congress and Exposition, IMECE 2005 - Orlando, FL, United States
Duration: Nov 5 2005Nov 11 2005

Publication series

NameAmerican Society of Mechanical Engineers, Micro-Electro Mechanical Systems Division, (Publications) MEMS
Volume7 MEMS
ISSN (Print)1096-665X

Other

Other2005 ASME International Mecahnical Engineering Congress and Exposition, IMECE 2005
CountryUnited States
CityOrlando, FL
Period11/5/0511/11/05

All Science Journal Classification (ASJC) codes

  • Mechanical Engineering
  • Electrical and Electronic Engineering
  • Control and Systems Engineering

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  • Cite this

    Mahdavi, A., & Mockensturm, E. M. (2005). A new hierarchical technique for the multiscale modeling of carbon nanostructures. In American Society of Mechanical Engineers, Micro-Electro Mechanical Systems Division, (Publications) MEMS (pp. 597-600). (American Society of Mechanical Engineers, Micro-Electro Mechanical Systems Division, (Publications) MEMS; Vol. 7 MEMS). https://doi.org/10.1115/IMECE2005-82988