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A Nanoscopic Approach to the Determination of the Elastic Constants of Cubic Crystals in first Strain Gradient Theory

Moosavian, Hashem | 2014

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 45966 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Mohammadi Shodja, Hossein
  7. Abstract:
  8. In many problems, the traditional elasticity cannot predict phenomenon such as nano-scale defects, surface effects, and stress concentration correctly. For example, analysis near the crack tip, dislocation and inhomogeneity shows inconsistent results because in this case values of stress go to infinity. Therefore for solving these kinds of problems, higher order continuum theories were introduced. The appearance of additional constants in the equations of motion can represent the atomic nature of materials. Furthermore, they can be utilized for determining properties of materials vibration with high frequency, granular materials, and polymers.First strain gradient theory introduced by Mindlin (1968) is one of the higher order continuum theories in which the nano-scale effects can be captured. This theory was presented with the assumption of small deformation and for the isotropic materials. In the formulation, additional constants are appeared which is dependent to the material properties. Due to the lack of experimental methods for determination of additional elastic constants, the application of first strain gradient theory restricts severely. Hence, determination of elastic constants has an important role in development of this theory. Recently, analytical methods have been developed based on atomistic view point. It has been shown that these methods can predict elastic constants with desirable accuracy.
    As an approximation, it can be assumed that the cubic crystals behavior are as the same as isotropic materials. Then in previous works cubic crystals were applied in this theory. But in this thesis, first strain gradient theory is formulated for cubic crystals instead of isotropic materials for the first time. It is useful formulation for determining of cubic material properties in accurate way. In the next part, by using atomic viewpoint the elastic constants can be calculated for various cubic crystals
  9. Keywords:
  10. Ab Initio Calculation ; First Strain Gradient Theory ; Lattice Dynamics Theory ; Cubic Crystals ; Elastic Constants

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