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Numerical Modeling of a Nano Crack in Fcc Solids Using RKPM Based Dipolar Gradient Elasticity
Shariatzadeh, Babak | 2009
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- Type of Document: M.Sc. Thesis
- Language: English
- Document No: 40221 (53)
- University: Sharif University of Technology, International Campus, Kish Island
- Department: Science and Engineering
- Advisor(s): Mohammadi Shodja, Hosain
- Abstract:
- In many structures, crack creation is one of the most significant fracture mechanisms. To predict these fracture mechanisms accurate numerical modeling is necssary. Finite Element Method (FEM) is one of the substantial methods in analysis of numerical fracture problems in recent past decades. But, this method has difficulties in remeshing of elements in each step of calculation in fracture mechanics or large deformation analysis. Therefore, the theory was defined that, without using elements, just with setting of characteristics nodes in geometry of problem, the differential equations can be solved. These methods are called Meshfree or Meshless methods. RKPM is a new meshfree method for solving the differential problems in recent years that is used in this project. The classical continuum mechanics fail to give an accurate solution near the crack tip, moreover it implies that a solid is able to sustain an infinite stress at the Griffith–Inglis crack tips, and also has infirmity to sense the size effect in nano scale. The material in micro scale is modeled through the generalized continuum theory of dipolar gradient elasticity or grade two theory or strain gradient elasticity. For the first time in this thesis this theory and RKPM are used simultaneously to numerically analysis a plane cracks in nano scale. It is expected that the proposed problem can effectively and accurately be solved by RKPM in microstructured and nano scaled solids. The stability and high convergence rate is also expected. Most of all, the success in accurate and efficient calculation of the stress distribution around the crack is quite valuable in enhancing the design of connections in structures.
- Keywords:
- Charachteristic Length ; Crack ; Meshless Method ; Reproducing Kernel Particle Method (RKPM) ; Nano-Scale Modeling ; Gradient Elasticity Theory
- محتواي پايان نامه
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- Thesis Babak Shariatzadeh.pdf
- Overview and Classification of Meshfree Methods
- Chapter 2 Overview of Reproducing Kernel Particle Method (RKPM)
- Chapter 3 Determination of particle volume and dilation parameter for each node
- Chapter 4 Correction of the shape function for discontinuous domains
- Chapter 5 Application of essential boundary conditions in RKPM formulation
- Chapter 6 Dipolar gradient elasticity
- Chapter 7 Concepts of crack in fracture mechanics
- Chapter 8 Applying Essential Boundary condition in RKPM
- Chapter 9 Numerical example of Strain Gradient Elasticity with RKPM
- Chapter 10 Numerical Modeling of Fracture Mechanics with RKPM and Strain Gradient Elasticity
- Chapter 11 Simulation and Results of Crack in Nanoscale
- Chapter 12 Conclusion and recommendation