Abstract
We discuss the dynamics of media with hysteretic stress-strain properties. First, experimental evidence of the hysteretic behavior of rock is presented. This evidence leads to a pattern of unifying behavior whose origin is within the “bond system” of the material, which includes small cracks, intergrain contacts and, the cement that holds the grains in place. Nonlinear response is evident over a large frequency interval (dc to several MHz at least), and it is significant from strains of plasticity down to the smallest measurable strains (order 10-8-10-9). Second, some models related to such a behavior are outlined. Finally, oscillations and waves in hysteretic media are discussed.
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REFERENCES
A. Andronov, A. Vitt, and S. Khaikin, Theory of Oscillations, Dover, New York (1987).
A. Gaponov L. Ostrovsky, and G. Freidman, Sov. Radiophysics (1967).
R. Guyer and P. Johnson, Physics Today, 52, 30 (1999).
L. Ostrovsky and P. Johnson, Riv. Nuovo Cimento (2001), in press.
L. Hilbert, T. Hwong, N. Cook, K. Nihei, and L. Myer, in: P.P. Nelson and S. E. Laubach (eds.), Rock Mechanics Models and Measurements Challenges from Industry, A.A.Balkema, Rotterdam (1994), p. 497.
J. Jaeger and N. Cook, in: Fundamentals of Rock Mechanics, 3rd Edition, Chapman and Hall, London (1979), p. 78.
R. Guyer, K. Mccall, G. Boitnott, L. Hilbert, and T. Plona, J. Geophys. Res., 102, 5281 (1997).
P. Johnson, B. Zinszner, and P. Rasolofosaon, J. Geophys. Res., 101(B5) (1996)
V. Nazarov, L. Ostrovsky, I. Soustova, and A. Sutin, Phys. Earth Planet. Interiors, 50, 65 (1988).
J. Tencate and T. Shankland, Geophys. Res. Lett., 23, 3019 (1996).
J. Tencate, J. Smith, and R. Guyer, Phys. Rev. Lett., 85, 1020 (2000).
K. Ishihara, Soil Behaviour in Earthquake Geotechnics, Clarendon Press, Oxford (1996).
V. Nazarov, L. Ostrovsky, I. Soustova, and A. Sutin, Acoust. Phys., 30, No. 5, 827 (1994).
S. V. Zimenkov and V. Nazarov, Izv., Fiz. Zemli, 29, 12 (1994).
R. Guyer, P. Johnson, and J. Tencate, Phys. Rev. Lett., 82, 3280 (1999).
I. Belyaeva, L. Ostrovsky, and V. Zaitsev, Nonlinear Processes in Geophysics, 4, 1 (1997).
L. Ostrovsky, P. Johnson, and T. Shankland, in: W. Lauterborn and T. Kurz (eds.), Nonlinear Acoustics at the Turn of the Millennium, ISNA 15, Göttingen, 1999, Amer. Inst. of Physics, Melville, N.Y., (2000), pp. 75-84.
K. A. Naugolnykh and L. A. Ostrovsky, Nonlinear Wave Processes in Acoustics, Cambridge Univ. Press, Cambridge-NewYork (1998).
L. Landau and E. Lifshits, Theory of Elasticity, 3rd edition, Pergamon Press, Oxford (1986).
S. Asano, J. Phys. Soc. Japan, 29, 952 (1970).
R. Guyer, K. McCall, G. Boitnott, L. Hilbert, and T. Plona, J. Geophys. Res., 102 5281 (1995).
I. Belyaeva, L. Ostrovsky, and E. Timanin, Acoust. Lett., 15(11), 221 (1992).
K. Van den Abeele, J. Carmeliet, P. Johnson, and B. Zinszner, J. Geophys. Res., (2000), submitted.
D. Johnson, H. Makse, N. Gland, and L. Schwartz, Physica B, 279, 134 (2000).
A. Granato and K. L*#x00FC;cke, J. Appl. Phys., 27 583 (1956).
V. Nazarov, Acoust. Phys., 43, 192 (1997).
K. Van den Abeele, P. Johnson, R. Guyer, and K. McCall, J. Acoust. Soc. Am., 101(4) 1885 (1997).
V. Gusev, C. Glorieux, W. Lauriks, and J. Thoen, Phys. Lett. A, 232 77 (1997).
V. Gusev, J. Acoust. Soc. Am., 107(6), 3047 (2000).
L. Ostrovsky, I. Soustova, and A. Sutin, Acustica, 5, 298 (1978).
K. Van den Abeele, P. Johnson, AND A. Sutin, Research on Nondestructive Evaluation, 12/1, 17 (2000).
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Ostrovsky, L.A., Johnson, P.A. Nonlinear Dynamics of Rock: Hysteretic Behavior. Radiophysics and Quantum Electronics 44, 450–464 (2001). https://doi.org/10.1023/A:1017953331645
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DOI: https://doi.org/10.1023/A:1017953331645