Bagherzadeh, Mahsa | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 43307 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mohammadi Shodja, Hossien
  7. Abstract:
  8. The present study aims at determining the elastic fields of ultra-small flaws and defects. These defects are often introduced undesirably in elastic solids during fabrication and their sizes are normally in the order of couple of nano-meters. In this work, the elastic fields around a circular nano-void subjected to a uniform farfield uniaxial tension, also the elastic fields of a nano-sized mode I crack under remote uniform loading are studied. In this paper the strain gradient theory developed by Mindlin and co-workers in 1960s is employed. According to this theory, the strain energy density assumes the form of a positive-definite function of the strain components and their first gradient. This theory on intrinsic or material length scales finds applications in the modeling of size-dependent phenomena. A major task of the current work is to implement first strain gradient elasticity into the meshless approaches RKPM and GRKPM. The results show significant departure from the predictions of standard fracture mechanics. In view of these results, it seems that the classical theory of elasticity is inadequate to analyze nanodefect. First, the void problem is taken into consideration. The problem is solved by numerical methods then the results are verified by Eshel, Rosenfeld study, plus dependency of stress concentration factor on different parameters is discussed. Finally, in second problem the J-integral in gradient elasticity context is evaluated. A decrease of its value is noticed in comparison with classical elasticity when crack length becomes comparable with material length scales which is called strengthening effect.
  9. Keywords:
  10. Nanocrack ; Reproducing Kernel Particle Method (RKPM) ; Generalized Reproducing Kernel Particle Method (GRKPM) ; Strain Gradient Theory ; Nano-Void

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