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Finite anti-plane shear deformation of nonlinear elastic composites reinforced with elliptic fibers

Avazmohammadi, R ; Sharif University of Technology | 2009

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  1. Type of Document: Article
  2. DOI: 10.1016/j.mechmat.2009.02.005
  3. Publisher: 2009
  4. Abstract:
  5. Exact solutions for nonlinear composites undergoing finite deformation are in general difficult to find. In this article, such a solution is obtained for a two-phase composite reinforced with elliptic fibers under anti-plane shear. The analysis is based on the theory of hyperelasticity with both phases characterized by incompressible neo-Hookean strain energies, and is carried out when the composite elliptic cylinder assemblage carries a confocal microgeometry. The problem for a class of compressible neo-Hookean materials is also studied. The analytical results for the stress and strain distributions are verified with finite element calculations where excellent agreement is found. We then derived the explicit relations for the macroscopic nominal stress tensor and the effective secant axial-shear moduli under finite deformation. To make contact with existing micromechanics theories, it is further demonstrated that, within the small-strain framework, the obtained axial-shear moduli with conformal arrangement coincide with those of the double-inclusion model [Hori, M., Nemat-Nasser, S., 1993. Double-inclusion model and overall moduli of multi-phase composites. Mech. Mater. 14, 189-206]. © 2009 Elsevier Ltd. All rights reserved
  6. Keywords:
  7. Analytical results ; Anti planes ; Anti-plane shear deformations ; Elastic composites ; Elliptic cylinders ; Elliptic fibers ; Exact solutions ; Finite deformations ; Finite element calculations ; Hyper elasticities ; Inclusion models ; Micro geometries ; Multi-phase composites ; Neo-hookean materials ; Nominal stress ; Nonlinear composites ; Shear modulus ; Stress and strain distributions ; Two-phase composites ; Elastic moduli ; Incompressible flow ; Shear deformation ; Shear strain ; Reinforced plastics
  8. Source: Mechanics of Materials ; Volume 41, Issue 7 , 2009 , Pages 868-877 ; 01676636 (ISSN)
  9. URL: https://www.sciencedirect.com/science/article/abs/pii/S0167663609000477