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Elliptic inhomogeneities and inclusions in anti-plane couple stress elasticity with application to nano-composites

Haftbaradaran, H ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1016/j.ijsolstr.2009.03.026
  3. Publisher: 2009
  4. Abstract:
  5. It is well-known that classical continuum theory has certain deficiencies in predicting material's behavior at the micro- and nanoscales, where the size effect is not negligible. Higher order continuum theories introduce new material constants into the formulation, making the interpretation of the size effect possible. One famous version of these theories is the couple stress theory, invoked to study the anti-plane problems of the elliptic inhomogeneities and inclusions in the present work. The formulation in elliptic coordinates leads to an exact series solution involving Mathieu functions. Subsequently, the elastic fields of a single inhomogeneity in conjunction with the Mori-Tanaka theory is employed to estimate the overall anti-plane shear moduli of composites with uni-directional elliptic cylindrical fibers. The dependence of the anti-plane elastic moduli on several important physical parameters such as size, aspect ratio and rigidity of the fiber, the characteristic length of the constituents, and the orientation of the reinforcements is analyzed. Based on the available data in the literature, certain nano-composite models have been proposed and their overall behavior estimated using the present theory. © 2009 Elsevier Ltd. All rights reserved
  6. Keywords:
  7. Nano-composites ; Anti-plane ; Anti-plane problem ; Characteristic length ; Classical continuum theory ; Couple stress ; Couple stress elasticity ; Couple stress theory ; Cylindrical fibers ; Elastic fields ; Elliptic coordinates ; Higher order continuum ; Inhomogeneities ; Inhomogeneity ; Mathieu functions ; Mori-tanaka theory ; Nano scale ; New material constants ; Physical parameters ; Series solutions ; Shear modulus ; Size effects ; Aspect ratio ; Continuum mechanics ; Geometry ; Nanocomposites ; Elastic moduli
  8. Source: International Journal of Solids and Structures ; Volume 46, Issue 16 , 2009 , Pages 2978-2987 ; 00207683 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/pii/S0020768309001619