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Hierarchical Multi-scale Analysis using Nonlinear Finite Element & its Application to Porous Media

Asgharzadeh, Mohammad Ali | 2012

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 42751 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Naghdabadi, Reza; Sohrabpour, Saeed
  7. Abstract:
  8. Porous materials, with diverse applications in engineering branches, are categorized as multi-scale. A multi-scale material is one which shows different structure and/or behavior in two or more different length scales. There are physical models which can calculate the macroscopic properties of such materials by using both the properties and volume fractions of the ingredients. However, the number of such theories which can handle problems in the fields of elasticity and hydrodynamics is much less; the fields in which the tensor orders of the properties are more than one. Fortunately, in recent years, a new method named "Computational Multi-scale Homogenization" has been offered to homogenize engineering materials without any restrictions of its precedents. According to the shortcomings found in the literature, this method is selected to analyze the behavior of porous materials as a heterogeneous media. To do so, the effect of the displacement field in a macro material point is transferred to the micro scale as displacement boundary conditions. Using the distribution of stress in the micro level, obtained by solving the boundary value problem of the micro scale using finite element, the equivalent stress is calculated by volume averaging. In addition, it is shown that the presented formulation satisfies Hill-Mandel Principle. Subsequently, a computer code is written to solve boundary value problems. The validity of the method is proven through solving some examples. For instance, predicting the behavior of porous materials in the elastic domain shows a difference of only 8% in comparison with Mori-Tanaka theory. In addition, the stress concentration factor for a hole in an infinite plate is simulated, which is in good agreement with experimental results, with less than 5% of error. Finally, and in addition to the main path, a closed form equation for the effective properties of porous materials in 2D is presented, which is 11% and 2% more than the results based on Mori-Tanaka theory, under plane stress and plane strain conditions, respectively
  9. Keywords:
  10. Porous Materials ; Micromechanics ; Multiscale Modeling ; Effective Medium Approximation ; Computational Homogenization ; Multiscale Finite Element Method

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