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

R. Avazmohammadi, R. Naghdabadi, George Weng

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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].

Original languageEnglish (US)
Pages (from-to)868-877
Number of pages10
JournalMechanics of Materials
Volume41
Issue number7
DOIs
StatePublished - Jul 1 2009

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Shear deformation
shear
composite materials
fibers
Fibers
Composite materials
Elastic moduli
inclusions
micromechanics
Micromechanics
strain distribution
stress tensors
Strain energy
stress distribution
Tensors
energy

All Science Journal Classification (ASJC) codes

  • Mechanics of Materials
  • Instrumentation
  • Materials Science(all)

Cite this

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abstract = "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].",
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Finite anti-plane shear deformation of nonlinear elastic composites reinforced with elliptic fibers. / Avazmohammadi, R.; Naghdabadi, R.; Weng, George.

In: Mechanics of Materials, Vol. 41, No. 7, 01.07.2009, p. 868-877.

Research output: Contribution to journalArticle

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AU - Weng, George

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AB - 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].

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