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TECHNICAL PAPERS

Finite Amplitude Azimuthal Shear Waves in a Compressible Hyperelastic Solid

[+] Author and Article Information
J. B. Haddow

Department of Mechanical Engineering, University of Victoria, Victora, BC V8W 3P6, Canada  

L. Jiang

Martec Ltd., 1888 Brunswick Street Suite 400, Halifax Nova Scotia B36 3J8 Canada

J. Appl. Mech 68(2), 145-152 (Jun 01, 2000) (8 pages) doi:10.1115/1.1334862 History: Received July 22, 1999; Revised June 01, 2000
Copyright © 2001 by ASME
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References

Polignone,  D. A., and Horgan,  C. O., 1994, “Pure Azimuthal Shear of Compressible Nonlinear Elastic Circular Tubes,” Q. Appl. Math., 52, pp. 113–131.
Beatty,  M. F., and Jiang,  Q., 1997, “On Compressible Materials Capable of Sustaining Axisymmetric Shear Deformation. Part 2, Rotational Shear of Isotropic Hyperelastic Materials,” J. Mech. Appl. Mech., 50, pp. 211–237.
Jiang,  X., and Ogden,  R. W., 1998, “On Azimuthal Shear of a Circular Cylindrical Tube of Compressible Elastic Material,” J. Mech. Appl. Mech., 51, pp. 143–158.
Vandyke,  T. J., and Wineman,  A. S., 1996, “Small Amplitude Sinusoidal Disturbances Superimposed on Finite Circular Shear of a Compressible, Non-Linearly Elastic Material,” Int. J. Eng. Sci., 34, pp. 1197–1210.
Haddow,  J. B., and Jiang,  L., 1996, “A Study of Finite Amplitude Plane Wave Propagation in a Rubber-Like Solid,” Wave Motion, 24, pp. 211–225.
Blatz,  P. J., and Ko,  W. L., 1962, “Application of Finite Elasticity to the Deformation of Rubbery Materials,” Trans. Soc. Rheol., 6, pp. 223–251.
Levinson,  M., and Burgess,  I. W., 1971, “A Comparison of Some Simple Constitutive Relations for Slightly Compressible Rubberlike Materials,” Int. J. Mech. Sci., 13, pp. 563–572.
Beatty,  M. F., and Stalnacker,  D. O., 1986, “The Poisson Function of Finite Elasticity,” ASME J. Appl. Mech., 53, pp. 807–813.
Whitham, G. B., 1974, Linear and Nonlinear Waves, John Wiley and Sons, New York.
van Leer,  B., 1979, “Towards the Ultimate Conservative Difference Scheme, V. A Second-Order Sequel to Godunov’s Method,” J. Comput. Phys., 32, pp. 101–136.
Sod, G. A., 1985, Numerical Methods in Fluid Mechanics, Cambridge University Press, London.

Figures

Grahic Jump Location
Relationships between γ and nondimensional radius R for nondimensional times 0.1, 0.2, 0.3, 0.4, 0.5 and f=1 and f=0.6
Grahic Jump Location
Relationships between nondimensional Vθ and nondimensional radius R for nondimensional times 0.1, 0.2, 0.3, 0.4, 0.5 and f=1 and f=0.6
Grahic Jump Location
Relationships between δ−1 and nondimensional radius R for nondimensional times 0.1, 0.2, 0.3, 0.4, 0.5
Grahic Jump Location
Relationships between nondimensional Vr and nondimensional radius R for nondimensional times 0.1, 0.2, 0.3, 0.4, 0.5
Grahic Jump Location
Relationships between λ−1 and nondimensional radius R for nondimensional times 0.1, 0.2, 0.3, 0.4, 0.5

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