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BRIEF NOTES

Large Shearing of a Prestressed Tube

[+] Author and Article Information
M. Zidi

Université Paris 12 Val de Marne, Faculté des Sciences et Technologie, CNRS ESA 7052, Laboratoire de Mécanique Physique, 61, avenue du Général De Gaulle, 94010 Creteil Cedex, Francee-mail: zidi@univ-paris.12.fr

J. Appl. Mech 67(1), 209-212 (Oct 12, 1999) (4 pages) doi:10.1115/1.321175 History: Received March 24, 1998; Revised October 12, 1999
Copyright © 2000 by ASME
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References

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Ogden,  R. W., Chadwick,  P., and Haddon,  E. W., 1973, “Combined Axial and Torsional Shear of a Tube of Incompressible Isotropic Elastic Material,” Q. J. Mech. Appl. Math., 24, pp. 23–41.
Mioduchowski,  A., and Haddow,  J. B., 1979, “Combined Torsional and Telescopic Shear of a Compressible Hyperelastic Tube,” ASME J. Appl. Mech., 46, pp. 223–226.
Abeyaratne,  R. C., 1981, “Discontinuous Deformation Gradients in the Finite Twisting of an Incompressible Elastic Tube,” J. Elast., 11, pp. 43–80.
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Antman,  S. S., and Heng,  G. Z., 1984, “Large Shearing Oscillations of Incompressible Nonlinearly Elastic Bodies,” J. Elast., 14, pp. 249–262.
Simmonds,  J. G., and Warne,  P., 1992, “Azimuthal Shear of Compressible or Incompressible, Nonlinearly Elastic Polar Orthotropic Tubes of Infinite Extant,” Int. J. Non-Linear Mech., 27, No. 3, pp. 447–467.
Tao,  L., Rajagopal,  K. R., and Wineman,  A. S., 1992, “Circular Shearing and Torsion of Generalized Neo-Hookean Materials,” IMA J. Appl. Math., 48, pp. 23–37.
Polignone,  D. A., and Horgan,  C. O., 1994, “Pure Azimuthal Shear of Compressible Nonlinearly Elastic Tubes,” Q. Appl. Math., 50, pp. 113–131.
Wineman,  A. S., and Waldron,  W. K., 1995, “Normal Stress Effects Induced During Circular Shear of a Compressible Nonlinear Elastic Cylinder,” Int. J. Non-Linear Mech., 30, No. 3, pp. 323–339.
Sensening,  C. B., 1965, “Nonlinear Theory for the Deformation of Prestressed Circular Plates and Rings,” Commun. Pure Appl. Math., XVIII, pp. 147–161.
Spencer, A. J. M., 1984, Continuum Theory of the Mechanics of Fibre-Reinforced Composites, Springer-Verlag, New York.
Cheref,  M., Zidi,  M., and Oddou,  C., 1995, “Caractérisation du Comportement Mécanique d’une Structure Structure Polymérique: Aide à la Conception de Prothèses Vascularies,” Arch. Physiol. Biochem., 103, p. C63.

Figures

Grahic Jump Location
Cross section of the tube in the stress-free (a), unloaded (b), and loaded configuration (c)
Grahic Jump Location
Azimuthal stresses distribution inside the wall without fibers (stresses normalized by σ(re),μ=0.166 Mpa,pi=0.0133 Mpa,τi=2 mm,τe=3 mm)
Grahic Jump Location
Azimuthal stresses distribution inside the wall with fibers (stresses normalized by σ(re),μ=0.166 Mpa,Ef=10 Mpa,pi=0.0133 Mpa,τi=2 mm,τe=3 mm)

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