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TECHNICAL PAPERS

Large Deformations of a Rotating Solid Cylinder for Non-Gaussian Isotropic, Incompressible Hyperelastic Materials

[+] Author and Article Information
C. O. Horgan

Applied Mechanics Program, Department of Civil Engineering, University of Virginia, Charlottesville, VA 22904 e-mail: coh8p@virginia.edu

G. Saccomandi

Dipartimento di Ingegneria dell’Innovazione, Università degli Studi di Lecce, 73100 Lecce, Italye-mail: giuseppe.saccomandi@unile.it

J. Appl. Mech 68(1), 115-117 (Jun 08, 2000) (3 pages) doi:10.1115/1.1349418 History: Received June 08, 2000
Copyright © 2001 by ASME
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References

Mark, J. E., and Erman, B., 1988, Rubberlike Elasticity: A Molecular Primer, John Wiley and Sons, New York.
Gent,  A. N., 1996, “A New Constitutive Relation for Rubber,” Rubber Chem. Technol., 69, pp. 59–61.
Boyce,  M. C., 1996, “Direct Comparison of the Gent and the Arruda-Boyce Constitutive Models of Rubber Elasticity,” Rubber Chem. Technol., 69, pp. 781–785.
Horgan,  C. O., and Saccomandi,  G., 1999, “Simple Torsion of Isotropic, Hyperelastic, Incompressible Materials With Limiting Chain Extensibility,” J. Elast., 56, pp. 159–170.
Horgan,  C. O., and Saccomandi,  G., 1999, “Pure Axial Shear of Isotropic Incompressible Nonlinearly Elastic Materials With Limiting Chain Extensibility,” J. Elast., 57, pp. 307–319.
Horgan,  C. O., and Saccomandi,  G., 2001, “Pure Azimuthal Shear of Isotropic Incompressible Hyperelastic Materials With Limiting Chain Extensibility,” Int. J. Non-Linear Mech., 36, pp. 465–475.
Knowles,  J. K., 1977, “The Finite Anti-Plane Shear Field Near the Tip of a Crack for a Class of Incompressible Elastic Solids,” Int. J. Fract., 13, pp. 611–639.
Erman,  B., and Mark,  J. E., 1988, “Use of Fixman-Alben Distribution Function in the Analysis of Non-Gaussian Rubber-Like Elasticity,” J. Chem. Phys., 89, pp. 3314–3316.
Chadwick,  P., Creasy,  C. F. M., and Hart,  V. G., 1977, “The Deformation of Rubber Cylinders and Tubes by Rotation,” J. Aust. Math. Soc. B, Appl. Math., 20, Series 13, pp. 62–96.
Ogden, R. W., 1984, Non-linear Elastic Deformations, Ellis Horwood, Chichester, UK, reprinted by Dover, New York, 1997.
Haughton,  D. M., and Ogden,  R. W., 1980, “Bifurcation of Finitely Deformed Rotating Cylinders,” Q. J. Mech. Appl. Math., 33, pp. 251–265.
Hunter, S. C., 1976, Mechanics of Continuous Media, Ellis Horwood, Chichester, UK.
Mott,  P. H., and Roland,  C. M., 1996, “Elasticity of Natural Rubber Networks,” Macromolecules, 29, pp. 6941–6945.

Figures

Grahic Jump Location
Plot of −M(λ)/μ versus λ for the power-law material n=3/2 (solid curve) and n=1/4 (dashed curve). The solid curve has the vertical axis as an asymptote as λ→0+.
Grahic Jump Location
Plot of −M(λ)/μ versus λ for the neo-Hookean and Gent material. The curve for the Gent material has the vertical line as an asymptote as λ→λm.

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