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Local Homogenization of 2D Foams with Circle-Based Voronoi Structures

Ramezani Goldiani, Majid | 2013

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 44346 (09)
  4. University: Sharif University of Technology
  5. Department: Civil Engineering
  6. Advisor(s): Vafai, Abolhassan; Shahbeyk, Sharif
  7. Abstract:
  8. The unique characteristics of solid foams make them ideal for both natural and man-made structures. The cellular structure of these materials allows for the construction of natural structures such as bone and wood that have high strength and use minimal primary materials. Their unique structure has inspired studies in the automotive and aerospace industries, leading to a new generation of lightweight materials. The focus of this study was the effects of the microstructure of foams on the macro mechanical response of specific structures. Homogenization methods are well suited for the study of these effects due to the random nature of the microstructures. One major problem in using numerical methods is the choice of a precise model for the microstructure of the foam. Computational homogenization methods that analyze part of the microstructure as an RVE using voronoi structures are important approaches due to the similarity between voronoi structures and the natural state of the microstructure of the foam. Circle-based voronoi diagrams are used due to their similarity with the foam structure because of its curved cellular edges. After initial loading, the RVE was found using finite element methods, as a structure consisting of curved edges with beam-like behavior. A local homogenization method was used in the lower level of the hierarchy to reach effects of microstructure on macroscopic behavior of foam. In this level of the analysis, each RVE is partitioned into several TVEs. Each intersection point of the voronoi diagram with half of the intersected edges are considered as a TVE that is an irregular hexagon. Assuming elastic material behavior, the effective stiffness components are calculated by analytically solving all of the TVEs under the calculated displacements from the RVE analysis in the higher level of the hierarchy. Finally, the effects of microstructure on macroscopic mechanical behavior of the material were studied for various microstructure cell sizes
  9. Keywords:
  10. Constitutive Model ; Local Homogenization ; Two Dimentional Foam ; Circle-Based Voronoi Diagram

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