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Multiscale Nonlinear Finite Element Analysis of Nanostructured Materials Based on Equivalent Continuum Mechanics

Ghanbari, Jaafar | 2004

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 40142 (08)
  4. University: Sharif University of Technology
  5. Department: Mechanical Engineering
  6. Advisor(s): Naghdabadi, Reza; Sohrabpour, Saeed
  7. Abstract:
  8. Nanostructured materials are a new kind of engineering materials which attracted researchers’ interest because of their interesting mechanical /physical properties, as well as controllable microstructural design ability for desired applications. These new materials are homogeneous at the macroscale but at the microstructural level, may have heterogeneities including common nanostructures. Because of multiscale nature of these materials, new multiscale methods should be developed and used for better understanding the behavior of them. Multiscale methods could be categorized into concurrent and hierarchical methods. In concurrent methods, the domain under study is explicitly divided into several subdomains in which specific theory governs. On the other hand, in hierarchical methods, each scale is present throughout the main domain. In the current dissertation, a hierarchical multiscale method based on nonlinear continuum mechanics is presented for the analysis of nanostructured materials. In the presented method, there is no border between the scales and the passage of the data is done using the averaging theorems and computational homogenization. This scheme consists of definition of two boundary value problems, one for macroscale (the scale in which the material exists homogeneously and we are interested in modeling the material behavior on that scale), and another for microscale (the scale in which the material becomes heterogeneous and microstructural constituents emerge). The coupling between these scales is done by using homogenization technique. At every material point in which the constitutive model is needed, a microscale boundary value problem is defined using a macroscopic kinematical quantity and solved. After the solution of the microscale problem, the macroscopic stress measure is calculated using the computational homogenization. At the macrolevel, no form of constitutive model is assumed since the constitutive response is obtained from the microscale analysis. At the microscale, there is no limitation on the form of constitutive models for the constituents. For carbon nanostructures, a constitutive model is presented using the modified Morse interatomic potential. Since the model is presented using large deformation finite elements, nonlinear behavior of nanostructured materials can be analyzed, which is not possible in the analytical homogenization methods. Using the presented scheme, two nanostructured materials (CNT/polymer nanocomposite and cortical bone) are analyzed and the results for elastic properties are compared with several experimental and analytical data
  9. Keywords:
  10. Carbon Nanostructures ; Nanocomposite ; Constitutive Model ; Multiscale Modeling ; Nonlinear Finite Element Method ; Nanostructured Materials

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