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Effective Shear Modulus of Elastic Solids Reinforced by Coated Elliptic Nanofibers in the Context of Couple Stress and Micropolar Theories

Alemi, Bita | 2018

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  1. Type of Document: Ph.D. Dissertation
  2. Language: English
  3. Document No: 50721 (53)
  4. University: Sharif University of Technology, International Campus, Kish Island
  5. Department: Science and Engineering
  6. Advisor(s): Mohammadi Shodja, Hossein
  7. Abstract:
  8. Nowadays, by adding a small amount of a desired nanomaterial to a matrix having certain properties one may design a multifunctional nanocomposites with a remarkably improved macroscopic properties of interest. The capability of conventional continuum theories in treating the problems of embedded ultra-small inhomogeneity with any of its dimensions comparable to the characteristic lengths of the involved constituent phases is questioned, mainly, on the grounds of the accuracy and the size effect. In this work, effort is firstly directed at the prediction of the macroscopic shear modulus of composites consisting of nano-/micro-size fibers of elliptic cross-sections via couple stress theory, a physically realistic theory that encompasses the size effect. Accurate estimation of the in-plane shear modulus of solids reinforced by nano-/micro-size elliptical multi-coated fibers in the context of micropolar theory is the second aim of this work. To this end, the fundamental equations of couple stress and micropolar elasticities in elliptic coordinates are derived and several fundamental elliptic inhomogeneity problems in plane elasticity are solved analytically. For the purpose of the application of these results to the study of the effective properties of the composites of interest, Mori-Tanaka theory is first reformulated in the mathematical framework of couple stress and micropolar theories. Subsequently, the overall shear modulus of solids reinforced by aligned as well as randomly oriented elliptic single-phase/multi-phase nanofibers will be predicted. The effects of the size, volume fraction, orientation, and the aspect ratio of the fibers and also the effects of characteristic lengths and rigidity of the constituent phases, and thickness of the coating layer of the fiber on the effective shear modulus of the composite are examined. In this work it is demonstrated that, composites with smaller size of fibers have larger shear modulus. Also it is found that, the effective shear modulus of composites with ribbon-shaped and circular fibers have respectively the maximum and minimum values
  9. Keywords:
  10. Size Effect ; Micropolar Hyper-Elasticity ; Couple Stress ; Shear Modulus ; Effective Shear Modulus ; Multi-Coated Elliptic Nanofibers

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