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BRIEF NOTES

Torsion of a Viscoelastic Cylinder

[+] Author and Article Information
R. C. Batra, J. H. Yu

Department of Engineering Science and Mechanics, M/C 0219, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061

J. Appl. Mech 67(2), 424-427 (Feb 01, 2000) (4 pages) doi:10.1115/1.1303824 History: Received March 09, 1999; Revised February 01, 2000
Copyright © 2000 by ASME
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References

Batra,  R. C., and Yu,  J. H., 1999, “Linear Constitutive Relations in Isotropic Finite Viscoelasticity,” J. Elast., 55, No. 1, pp. 73–77.
Christensen,  R. M., 1980, “A Nonlinear Theory of Viscoelasticity for Applications to Elastomers,” ASME J. Appl. Mech., 47, pp. 762–768.
Bernstein,  B., Kearsley,  E. A., and Zapas,  L. J., 1963, “A Study of Stress Relaxation With Finite Strain,” Trans. Soc. Rheol., 7, pp. 391–410.
Fosdick,  R. L., and Yu,  J. H., 1998, “Thermodynamics, Stability and Non-linear Oscillations of Viscoelastic Solids—II. History Type Solids,” Int. J. Non-Linear Mech., 33, No. 1, pp. 165–188.
Bell, J. F., 1973, “The Experimental Foundation of Solid Mechanics,” Handbuch der Physik, VIa/1, C. Truesdell, ed., Springer-Verlag, Berlin, pp. 1–813.
Batra,  R. C., 1998, “Linear Constitutive Relations in Isotropic Finite Elasticity,” J. Elast., 51, pp. 243–245.
Batra, R. C., 2000, “Comparison of Results From Four Linear Constitutive Relations in Isotropic Finite Elasticity,” Int. J. Nonlinear Mech., accepted for publication.
Ericksen,  J. L., 1954, “Deformations Possible in Every Isotropic Incompressible Perfectly Elastic Body,” Z. Angew. Math. Phys., 5, pp. 466–486.
Carroll,  M. M., 1967, “Controllable Deformations of Incompressible Simple Materials,” Int. J. Eng. Sci., 5, pp. 515–525.
Christensen,  R. M., 1968, “On Obtaining Solutions in Nonlinear Viscoelasticity,” ASME J. Appl. Mech., 35, pp. 129–133.
Truesdell, C., and Noll, W., 1965, The Non-Linear Field Theories of Mechanics, Handbook of Physics, Vol. III/3, Springer, New York.
Lenoe,  E. M., Heller,  R. A., and Fruedenthal,  A. M., 1965, “Viscoelastic Behavior of a Filled Elastomer in the Linear and Nonlinear Range,” Trans. Soc. Rheol., 9, No. 2, pp. 77–102.

Figures

Grahic Jump Location
Average shear stress versus shear strain curves computed from constitutive relations (5a) and (5b) and the test data of Lenoe et al. 12. The test data is indicated as dots.
Grahic Jump Location
The normalized energy loss/cycle per unit length of the cylinder as a function of the reciprocal of the relaxation time and the angular frequency
Grahic Jump Location
Energy loss/cycle per unit length of the cylinder as a function of the forcing frequency for the polyurethane rubber tested by Lenoe et al. 12

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