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Calculation of the additional constants for fcc materials in second strain gradient elasticity: Behavior of a nano-size bernoulli-euler beam with surface effects

Shodja, H. M ; Sharif University of Technology | 2012

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  1. Type of Document: Article
  2. DOI: 10.1115/1.4005535
  3. Publisher: 2012
  4. Abstract:
  5. In addition to enhancement of the results near the point of application of a concentrated load in the vicinity of nano-size defects, capturing surface effects in small structures, in the framework of second strain gradient elasticity is of particular interest. In this framework, sixteen additional material constants are revealed, incorporating the role of atomic structures of the elastic solid. In this work, the analytical formulations of these constants corresponding to fee metals are given in terms of the parameters of Sutton-Chen interatomic potential function. The constants for ten fcc metals are computed and tabulized. Moreover, the exact closed-form solution of the bending of a nano-size Bernoulli-Euler beam in second strain gradient elasticity is provided; the appearance of the additional constants in the corresponding formulations, through the governing equation and boundary conditions, can serve to delineate the true behavior of the material in ultra small elastic structures, having very large surface-to-volume ratio. Now that the values of the material constants are available, a nanoscopic study of the Kelvin problem in second strain gradient theory is performed, and the result is compared quantitatively with those of the first strain gradient and traditional theories
  6. Keywords:
  7. Bending ; Characteristic lengths: nano beam ; Sutton-Chen interatomic potential function ; Analytical formulation ; Bernoulli-Euler beam ; Characteristic length ; Closed form solutions ; Concentrated load ; Elastic solids ; Elastic structures ; FCC metals ; Governing equations ; Interatomic potential function ; Material constant ; Nano-size ; Nano-size defects ; Point of application ; Strain gradient elasticity ; Strain gradient theory ; Strain gradients ; Surface effect ; Surface-to-volume ratio ; Ultra-small ; Bending (forming) ; Strain measurement ; Surface defects ; Surfaces
  8. Source: Journal of Applied Mechanics, Transactions ASME ; Volume 79, Issue 2 , 2012 ; 00218936 (ISSN)
  9. URL: http://appliedmechanics.asmedigitalcollection.asme.org/article.aspx?articleid=1421426