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TECHNICAL PAPERS

Transient Green’s Function Behavior for a Prestressed Highly Elastic Half-Space

[+] Author and Article Information
L. M. Brock

Mechanical Engineering, University of Kentucky, Lexington, KY 40506

J. Appl. Mech 68(2), 162-168 (Aug 28, 2000) (7 pages) doi:10.1115/1.1357167 History: Received February 23, 2000; Revised August 28, 2000
Copyright © 2001 by ASME
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References

Achenbach, J. D., Pao, Y.-H., and Tiersten, H. F., 1976, “Applications of Elastic Waves in Electrical Devices, Non-Destructive Testing, and Seismology,” NSF Workshop Report, Northwestern University.
Pao, Y.-H., 1987, “Theory of Acoustoelasticity and Acoustoplasticity,” Solid Mechanics Research for Quantitative Non-Destructive Evaluation, J. D. Achenbach and Y. Rajapakse, eds., Martinus Nijhoff, Dordrecht, pp. 257–273.
Green, A. E., and Zerna, W., 1968, Theoretical Elasticity, 2nd ed., Oxford University, Oxford, UK.
Beatty,  M. F., and Usmani,  S., 1975, “On the Indentation of a Highly Elastic Half-Space,” Q. J. Mech. Appl. Math., 28, pp. 47–62.
Truesdell, C., and Noll, W., 1965, “The Non-Linear Field Theories of Mechanics,” Handbuch der Physik, Vol. III/3, W. Flugge, ed., Springer-Verlag, Berlin.
Hibbeler, R. C., 1997, Mechanics of Materials, 3rd ed., Prentice-Hall, Englewood Cliffs, NJ.
Achenbach, J. D., 1973, Wave Propagation in Elastic Solids, North-Holland, Amsterdam.
Sneddon, I. N., 1972, The Use of Integral Transforms, McGraw-Hill, New York.
van der Pol, B., and Bremmer, H., 1950, Operational Calculus Based on the Two-Sided Laplace Integral, Cambridge University Press, Cambridge, UK.
Hayes,  M. A., and Rivlin,  R. S., 1961, “Surface Waves in Deformed Elastic Material,” Arch. Ration. Mech. Anal., 8, pp. 358–380.
Dowaikh,  M. A., and Ogden,  R. W., 1991, “On Surface Waves in a Compressible Elastic Half-Space,” Stab. Appl. Analy. Continuous Media, 1, pp. 27–44.
deHoop,  A. T., 1960, “A Modification of Cagniard’s Method for Seismic Pulse Problems,” Appl. Sci. Res., B8, pp. 349–356.
Georgiadis,  H. G., and Barber,  J. R., 1993, “On the Super-Rayleigh/Subseismic Elastodynamic Indentation Problem,” J. Elast., 31, pp. 141–161.
Brock,  L. M., and Georgiadis,  H. G., 2000, “Sliding Contact With Friction on a Thermoelastic Solid at Subsonic and Supersonic Speeds,” J. Therm. Stresses, 23, pp. 629–633.
Brock,  L. M., 1999, “Sliding Contact With Friction at Arbitrary Constant Speeds on a Pre-Stressed Highly Elastic Half-Space,” J. Elast., 57, pp. 105–132.
Brock,  L. M., 1999, “Rapid Sliding Indentation With Friction of a Pre-Stressed Thermoelastic Material,” J. Elast., 53, pp. 161–188.

Figures

Grahic Jump Location
Isotropic compressible neo-Hookean material in axial loading
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(a) Stationary loads suddenly applied to surface, (b) surface loads translating on surface
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(a) Cagniard contour for Ak-terms in displacement, (b) Cagniard contours for Bk-terms in displacement
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Nondimensionalized wave speeds versus prestress
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(a) Wave pattern for transonic load speed, (b) wave pattern for supersonic load speed

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