Multi-scale modeling of surface effect via the boundary Cauchy-Born method

Qomi, M. J. A ; Sharif University of Technology | 2011

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  1. Type of Document: Article
  2. DOI: 10.1002/nme.2995
  3. Publisher: 2011
  4. Abstract:
  5. In this paper, a novel multi-scale approach is developed for modeling of the surface effect in crystalline nano-structures. The technique is based on the Cauchy-Born hypothesis in which the strain energy density of the equivalent continua is calculated by means of inter-atomic potentials. The notion of introducing the surface effect in the finite element method is based on the intrinsic function of quadratures, called as an indicator of material behavior. The information of quadratures is derived by interpolating the data from probable representative atoms in their proximity. The technique is implemented by the definition of reference boundary CB elements, which enable to capture not only the surface but also the edge and corner effects. As the surface effect is important in small-scale simulation, the relative number of boundary CB elements increases which leads to predomination of boundary effects in the model. In order to implement the equivalent continua in boundary value problems, the updated-Lagrangian formulation of nonlinear finite element is derived. The numerical simulation of the proposed model together with the direct comparison with fully atomistic model indicates that the technique provides promising results for facile modeling of boundary effects and investigating its effect on the mechanical response of metallic nano-scale devices
  6. Keywords:
  7. Atomistic models ; Boundary Cauchy-Born ; Boundary effects ; Cauchy-Born hypothesis ; Corner effects ; Interatomic potential ; Intrinsic functions ; Lagrangian formulations ; Material behavior ; Mechanical response ; Multi-scale approaches ; Multi-scale Modeling ; Nanoscale device ; Non-linear finite elements ; Numerical simulation ; Strain energy density ; Surface effect ; Computer simulation ; Finite element method ; Molecular dynamics ; Surfaces
  8. Source: International Journal for Numerical Methods in Engineering ; Volume 85, Issue 7 , August , 2011 , Pages 827-846 ; 00295981 (ISSN)
  9. URL: http://onlinelibrary.wiley.com/doi/10.1002/nme.2995/abstract