Advertisement

Nonlinear Impulses in Particulate Materials

  • Vitali F. Nesterenko
Chapter
Part of the High-Pressure Shock Compression of Condensed Matter book series (SHOCKWAVE)

Abstract

Impulse propagation in granular (particular) materials due to the loading under impact or contact explosion is of practical interest for many applications. For example, granular bed from iron shot is used for the damping of contact explosions during technological operations in explosive chambers. It effectively prevents the chamber wall from the high-amplitude shock wave. The propagation and reflection of nonlinear waves with large amplitudes in sand or soil is important for the detection of foreign objects. The nature of waves in these materials is also of general interest because they represent the collective dynamic response strongly effected by mesostructure. At the same time, these materials pose some fundamental questions which demand reconsideration of the basic foundation of wave dynamics including shock-wave propagation and shock dynamics particularly.

Keywords

Solitary Wave Granular Material Phase Speed Granular Medium Force Chain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Albert, J.P., and Bona, J.L. (1991) Comparisons Between Model Equations for Long Waves. Journal of Nonlinear Science, 1, pp. 345–374.MathSciNetADSzbMATHGoogle Scholar
  2. Anderson, G.D. (1964) Ph.D. thesis, Washington State University, Pullman.Google Scholar
  3. Apalikov, Yu.I., Bronovskii G.A., Konon Yu.A., et al. (1983) Support for Explosive Cladding of Metallic Surfaces. Patent USSR (A.C. 330702A SSSR, MKI B23K20/08), Discoveries, Inventions, no. 24, p. 200 (in Russian).Google Scholar
  4. Asano, N. (1974) Wave Propagation in Non-Uniform Media. Prog. Theor. Phys., Supplement No. 55.Google Scholar
  5. Balk, A.M., Cherkaev, A.V., and Slepyan, L.I. (2001) Dynamics of Chains with Non-Monotone Stress-Strain Relations. II. Nonlinear Waves and Waves of Phase Transition. J. Mech. Phys. Solids, 49, pp. 149–171.MathSciNetADSzbMATHGoogle Scholar
  6. Bardenhagen, S., and Triantafyllidis, N. (1994) Derivation of Higher Order Gradient Continuum Theories in 2,3-D Non-Linear Elasticity from Periodic Lattice Models. J. Mech. Phys. Solids, 42, no. 1, pp. 111–139.MathSciNetADSzbMATHGoogle Scholar
  7. Bardenhagen, S.G., and Brackbill, J.U. (1998) Dynamic Stress Bridging in Granular Material. J. Applied Physics, 83, no. 11, pp. 5732–5740.ADSGoogle Scholar
  8. Belyaeva, I.Yu., Zaitsev, V.Yu., and Ostrovskii, L.A. (1993) Nonlinear Acoustoelastic Properties of Granular Media. Acoustical Physics, 39, no. 1, pp. 11–15.ADSGoogle Scholar
  9. Belyaeva, I.Yu., Zaitsev, V.Yu., and Timanin, E.M. (1994) Experimental Study of Nonlinear Elastic Properties of Granular Media with Nonideal Packing. Acoustical Physics, 40, no. 6, pp. 789–793.ADSGoogle Scholar
  10. Benjamin, T.B., Bona, J.L., and Mahony, J.J. (1972) Model Equations for Long Waves in Nonlinear Dispersive Systems. Philosophical Transactions of the Royal Society of London A. Mathematical and Physical Sciences, 272, no. 1220, pp. 47–78.MathSciNetADSzbMATHGoogle Scholar
  11. Benson, D.J. (1994) An Analysis by Direct Numerical Simulation of the Effects of Particle Morphology on the Shock Compression of Copper Powder. Modelling Simul. Mater. Sci. Eng. 2, pp. 535–550.ADSGoogle Scholar
  12. Bernoulli, D. (1738) Theoremata de Oscillationibus Corporum Filo Flexili Connexorum et Catenae Verticaliter Suspensae. Comm. Acad. Sci. Petrop., 6, pp. 108–122. English translation: in The Evolution of Dynamics: Vibration Theory from 1687 to 1742. 1981, Springer-Verlag, New York, pp. 156–176.Google Scholar
  13. Bernoulli, D. (1741) Letter of 28 January 1741, from Correspondance Mathematique et Physique de Quelques Celebres Geometres du XVIII eme Siecle, vol. 2, St. Petersburg, 1843. Facs. rep. Johnson, New York, 1968. English translation: In: Cannon, J.T., and Dostrovsky, S. (1981) The Evolution of Dynamics: Vibration Theory from 1687 to 1742. Springer-Verlag, New York, p. 46.Google Scholar
  14. Bland, D.R. (1969) Nonlinear Dynamic Elasticity. Blaisdell, New York.zbMATHGoogle Scholar
  15. Bogdanov A.N., and Skvortsov A.T. (1992) Nonlinear Elastic Waves in a Granular Medium. Journal de Physique, Coll. C1, 2, pp. C1–779-C1–782.Google Scholar
  16. Bona, J.L., Pritchard, W.G., and Scott, L.R. (1983) A Comparison of Solutions of Two Model Equations for Long Waves. Proceedings of the AMS-SIAM Conference on Fluid Dynamical Problems in Astrophysics and Geophysics, Chicago, July 1981. Lectures in Applied Mathematics, 20, (Edited by N. Lebovitz). American Mathematical Society, Providence, RI, pp. 235–267.Google Scholar
  17. Boutreux, T., Raphael, E., and de Gennes, P.G. (1997) Propagation of a Pressure Step in a Granular Material; The Role of Wall Friction. Phys. Rev. B, 55, no. 5, pp. 5759–5773.ADSGoogle Scholar
  18. Brandt, H. (1955) A Study of the Speed of Sound in Porous Granular Media. ASME Journal of Applied Mechanics, 22, pp. 479–486.zbMATHGoogle Scholar
  19. Chapman, S. (1960) Misconception Concerning the Dynamics of the Impact Ball Apparatus. Am. J. Phys., 28, no. 8, pp. 705–711.ADSGoogle Scholar
  20. Chatterjee, A. (1999) An Asymptotic Solution for Solitary Waves in a Chain of Elastic Spheres. Phys. Rev. B, 59, no. 5, pp. 5912–5919.ADSGoogle Scholar
  21. Chen, P.J. (1973) Growth and Decay of Waves in Solids. In: Encyclopedia of Physics (Edited by S. Fluegge and C. Truesdell), Vol. VI a/3. Springer-Verlag, Berlin.Google Scholar
  22. Coleman, B.D. (1971a) On Retardation Theorems. Archive for Rational Mechanics and Analysis, 43, pp. 1–23.MathSciNetADSzbMATHGoogle Scholar
  23. Coleman, B.D. (1971b) A Mathematical Theory of Lateral Sensory Inhibition. Archive for Rational Mechanics and Analysis, 43, pp. 79–100.MathSciNetADSzbMATHGoogle Scholar
  24. Coleman, B.D. (1983) Necking and Drawing in Polymeric Fibers Under Tension. Archive for Rational Mechanics and Analysis, 83, pp. 115–137.MathSciNetADSzbMATHGoogle Scholar
  25. Coleman, B.D. (1985) On the Cold Drawing of Polymers. Comp. & Maths. With Appls., 11, nos. 1–3, pp. 35–65.zbMATHGoogle Scholar
  26. Coste, C, Falcon, E., and Fauve, S. (1997) Solitary Waves in a Chain of Beads Under Hertz Contact. Physical Review E, 56, no. 5, pp. 6104–6117.ADSGoogle Scholar
  27. Coste, C, and Gilles, B. (1999) On the Validity of Hertz Contact Law for Granular Material Acoustics. The European Physical Journal B, 7, pp. 155–168.ADSGoogle Scholar
  28. Cristescu, N. (1967) Dynamic Plasticity. North-Holland, Amsterdam.zbMATHGoogle Scholar
  29. Dash, P.C., and Patnaik, K. (1981) Solitons in Nonlinear Diatomic Lattices. Progress in Theoretical Physics, 65, no. 5, pp. 526–1541.Google Scholar
  30. de Gennes, P.G. (1996) Static Compression of a Granular Medium: The ‘Soft” Shell Model. Europhys. Lett. 5, no. 2, pp. 145–149.Google Scholar
  31. Deresiewicz, H. (1958) Stress-Strain Relations for a Simple Model of a Granular Medium. ASME Journal of Applied Mechanics, 25, pp. 402–406.zbMATHGoogle Scholar
  32. Digby, P.J. (1981) The Effective Elastic Moduli of Porous Granular Rocks. ASME Journal of Applied Mechanics, 48, pp. 803–808.ADSzbMATHGoogle Scholar
  33. Dinda, P.T., and Remoissenet, M. (1999) Breather Compactons in Nonlinear Klein-Gordon Systems. Phys. Rev. E, 60, no. 5, pp. 6218–6221.ADSGoogle Scholar
  34. Druzhinin, O.A., and Ostrovskii, L.A. (1991) Solitons in Discrete Lattices. Physics Letters A, 160, pp. 357–362.ADSGoogle Scholar
  35. Duffy, J., and Mindlin, R.D. (1957) Stress-Strain Relations and Vibrations of a Granular Medium. ASME Journal of Applied Mechanics, 24, pp. 585–593.MathSciNetGoogle Scholar
  36. Dusuel, S., Michaux, P., and Remoissenet, M. (1998) From Kinks to Compactonlike Kinks. Phys. Rev. E, 57, no. 2, pp. 2320–2326.ADSGoogle Scholar
  37. Duvall, G.E., Manvi, R., and Lowell, S.C. (1969) Steady Shock Profiles in a One-Dimensional Lattice. Journal of Applied Physics, 40, no. 9, pp. 3771–3775.ADSGoogle Scholar
  38. Falcon, E. (1997) Comportements Dynamiques Associes au Contact de Hertz: Processus Collectifs de Collision et Propagation D’Ondes Solitaires Dans les Milieux Granulaires. These 191–97, Diplome de Doctorat. L’Ecole Normale Superieure de Lyon.Google Scholar
  39. Falcon, E., Laroche, C, Fauve, S., and Coste, C. (1998a) Behavior of One Inelastic Ball Bouncing Repeatedly off the Ground. The European Physical Journal B, 3, pp. 45–57.ADSGoogle Scholar
  40. Falcon, E., Laroche, C, Fauve, S., and Coste, C. (1998b) Collision of a 1-D Column of Beads with a Wall. The European Physical Journal B, 5, pp. 111–131.ADSGoogle Scholar
  41. Fermi, E., Pasta, J.R., and Ulam, S.M. (1965) Studies of Non-Linear Problems. Technical Report. LA-1940, Los Alamos National Laboratory. Reprinted in Collected Works of E. Fermi, vol. II. University of Chicago Press, pp. 978–988.Google Scholar
  42. Filippov, A.T. (2000) The Versatile Soliton. Birkhauser, Boston.zbMATHGoogle Scholar
  43. Friesecke, G., and Wattis, J.A.D. (1994) Existence Theorem for Solitary Waves on Lattices. Communications in Mathematical Physics, 161, no. 2, pp. 391–418.MathSciNetADSzbMATHGoogle Scholar
  44. Gassmann, F. (1951) Elastic Waves Through a Packing of Spheres. Geophysics, 16, pp. 673–685.ADSGoogle Scholar
  45. Gavrilyuk, S.L. (1989) Modulation Equations for a Mixture of Gas Bubbles in an Incompressible Liquid. Prikl. Mekh. Tekh. Fiz., 30, no. 2, pp. 86–92 (in Russian). English translation: Journal of Applied Mechanics and Technical Physics (JAM) 1989, September, pp. 247–253.Google Scholar
  46. Gavrilyuk, S.L., and Nesterenko, V.F. (1993) Stability of Periodic Excitations for One Model of “Sonic Vacuum.” Prikl. Mekh. Tekh. Fiz., 34, no. 6, pp. 45–48 (in Russian). English translation: Journal of Applied Mechanics and Technical Physics(JAM) no. 6, 1993, pp. 784–787.zbMATHGoogle Scholar
  47. Gavrilyuk, S.L., and Serre, D. (1995) A Model of a Plug-Chain System Near the Thermodynamic Critical Point: Connection with the Korteweg Theory of Capillarity and Modulation Equations. Proceedings of IUTAM Symposium on Waves in Liquid/Gas and Liquid/Vapor Two-Phase Systems (Edited S. Morioka and L.van Wijngaarden), Kyoto, Japan, 1994. Kluwer Academic, Dodrecht, pp. 419–428.Google Scholar
  48. Gavrilyuk, S.L., and Shugrin, S.M. (1996) Media with Equations of State that Depend on Derivatives. PrikL Mekh. Tekh. Fiz., 37, no. 2, pp. 35–49 (in Russian).MathSciNetzbMATHGoogle Scholar
  49. Gavrilyuk, S.L., and Shugrin, S.M. English translation: Journal of Applied Mechanics and Technical Physics (JAM) 1996, 37, no. 2, pp. 177–189.MathSciNetADSGoogle Scholar
  50. Gilles, B., and Coste, C. (2001) Nonlinear Elasticity of a 2-D Regular Array of Beads. Powders and Grains (submitted).Google Scholar
  51. Goddard, J.D. (1990) Nonlinear Elasticity and Pressure-Dependent Wave Speeds in Granular Media. Proc. R. Soc. London A, 430, pp. 105–131.ADSzbMATHGoogle Scholar
  52. Godunov, S.K. (1961) An Interesting Class of Quasiliner Systems. Dokl. Akad. Nauk SSSR, 139, no. 3, pp. 521–523 (in Russian).MathSciNetGoogle Scholar
  53. Goldsmith, W. (1960) Impact. Arnold, London.zbMATHGoogle Scholar
  54. Goodman, M.A., and Cowin S.C. (1972) A Continuum Theory for Granular Materials. Archive for Rational Mechanics and Analysis, 44, pp. 249–266.MathSciNetADSzbMATHGoogle Scholar
  55. Gradshteyn, I.S., and Ryzhik I.M. (1980) Table of Integrals, Series, and Products. Academic Press, San Diego-Toronto, Harcourt Brace Jovanovich, p. 131.zbMATHGoogle Scholar
  56. Groshkov, A.L., Kalimulin, R.R., Shalashov, G.M., and Shemagin, V.A. (1990) Nonlinear Interbore-Hole Probing with Modulation of Acoustic Wave by Seismic Fields. Izvestiya AN SSSR, 313, no. 1, p. 63–65 (in Russian).Google Scholar
  57. Hammack, J.L. (1973) A Note on Tsunamis: Their Generation and Propagation in an Ocean of Uniform Depth. J. Fluid Mech., 60, pp. 769–799.ADSzbMATHGoogle Scholar
  58. Hammack, J. L., and Segur, H. (1974) The Korteveg-de Vries Equation and Water Waves. Part 2. Comparison with Experiments. J. Fluid Mech., 65, pp. 289–314.MathSciNetADSzbMATHGoogle Scholar
  59. Hara, G. (1935) Theorie der Akustischen Schwingungsausbreitung in Gekornten Substanzen und Experimentelle Untersuchungen an Kohlepulver. Elektrische Nachrichtentechnik, 12, pp. 191–200.Google Scholar
  60. Hascoet, E, Herrmann, HJ., and Loreto, V. (1999) Shock Propagation in a Granular Chain. Phys. Rev. E, 59, no. 3, pp. 3202–3206.ADSGoogle Scholar
  61. Hascoet, E., and Herrmann, H.J. (2000) Shocks in Non-Loaded Bead Chains With Impurities. The European Physical Journal B, 14, pp. 183–190.ADSGoogle Scholar
  62. Herrmann, F., and Schmalzle, P. (1981) Simple Explanation of a Well-Known Collision Experiment. Am. J. Phys., 49, no. 8, pp. 761–764.ADSGoogle Scholar
  63. Herrmann, F., and Seitz, P. (1982) How Does the Ball-Chain Work? Am. J. Phys., 50, no. 11, pp. 977–981.ADSGoogle Scholar
  64. Herrmann, H.J., Stauffer, D., and Roux, S. (1987) Violation of Linear Elasticity due to Randomness. Europhys. Lett. 3, no. 3, pp. 265–267.ADSGoogle Scholar
  65. Hill, T.G., and Knopoff, L. (1980) Propagation of Shock Waves in One-Dimensional Crystal Lattices. Journal of Geophysical Research, 85, no. B12, pp. 7025–7030.ADSGoogle Scholar
  66. Hinch E.J., and Saint-Jean S. (1999) The Fragmentation of a Line of Balls by an Impact. Proc. R. Soc. Lond. A, 455, pp. 3201–3220.MathSciNetADSzbMATHGoogle Scholar
  67. Hong, J., Ji, J.-Y., and Kim, H., (1999) Power Laws in Nonlinear Chain under Gravity. Phys. Rev. Lett., 82, no. 15, pp. 3058–3061.ADSGoogle Scholar
  68. Iida, K. (1939) Velocity of Elastic Waves in a Granular Substance. Bulletin of the Earthquake Research Institute, Japan, 17, pp. 783–808.Google Scholar
  69. Ipatiev, A.S., Kosenkov, A.P., Nesterenko, V.F., Meshcheriakov, Y.P., and Afanasenko, S.I. (1986) Experimental Investigation of Fracture Characteristics of Metal Plates with Semicylindrical Grooves at Explosive Loading with Contact Surface Charges. In: Proc. IX Intern. Conf on High Energy Rate Fabrication (Edited by V.F. Nesterenko and I.V. Yakovlev), USSR Academy of Sciences, Siberian Division, Novosibirsk, pp. 64–70.Google Scholar
  70. Jaeger, H.M., and Nagel, S.R. (1992) Physics of the Granular State. Science, 20, 255, pp. 1523–1531.Google Scholar
  71. Jaeger, H.M., and Nagel, S.R. (1996) Granular Solids, Liquids, and Gases. Reviews of Modern Physics, 68, no. 4, pp. 1259–1273.ADSGoogle Scholar
  72. Jia, X., Caroli, C, and Velicky, B. (1999) Ultrasound Propagation in Externally Stressed Granular Media. Phys. Rev. Letters, 82, no. 9, pp. 1863–1866.ADSGoogle Scholar
  73. Johnson, K.L. (1987) Contact Mechanics. Cambridge University Press, New York.Google Scholar
  74. Kivshar, Y.S. (1993) Intrinsic Localized Models as Solitons with a Compact Support. Phys. Rev. E, 48, no. 1, pp. R43-R45.MathSciNetADSGoogle Scholar
  75. Korteweg, D.J., and de Vries, G. (1895) On the Change of Form of Long Waves Advancing in a Rectangular Canal, and on an New Type of Long Stationary Waves. London, Edinburgh and Dublin Philosophical Magazine and Journal of Science, ser. 5, 39, pp. 422–443.zbMATHGoogle Scholar
  76. Kruskal, M. (1975) Nonlinear Wave Equations. In: Dynamical Systems, Theory and Applications, Lecture Notes in Physics, vol. 38. Springer-Verlag, Heidelberg, pp. 310–354.Google Scholar
  77. Kunin, I.A. (1975) Theory of Elastic Media with Microstructure. Nauka, Moscow (in Russian).Google Scholar
  78. Kuwabara, G., and Kono, K. (1987) Restitution Coefficient in a Collision between Two Spheres. Jap. J. Appl. Phys. 26, no. 8, pp. 1230–1233.ADSGoogle Scholar
  79. Landau, L.D., and Lifshitz E.M. (1976) Mechanics. Translated from the Russian by J.B. Sykes and J.S. Bell, 3rd ed. Pergamon Press, Oxford.Google Scholar
  80. Landau, L.D., and Lifshitz E.M. (1995) Theory of Elasticity. Translated from the Russian by J.B. Sykes and W.H. Reid, 3rd English ed. Revised and enlarged by E.M. Lifshitz, A.M. Kosevich, and L.P. Pitaevskii. Butterworth, Oxford; Heinemann, Boston.Google Scholar
  81. Lazaridi, A.N., and Nesterenko, V.F. (1985) Observation of a New Type of Solitary Waves in a One-dimensional Granular Medium. Prikl. Mekh. Tekh. Fiz., 26, no. 3, pp. 115–118 (in Russian).English translation: Journal of Applied Mechanics and Technical Physics (JAM), 1985, pp. 405–408.Google Scholar
  82. Lee, M.H., Florencio, J. Jr., and Hong, J. (1989) Dynamic Equivalence of a Two-Dimensional Quantum Electron Gas and a Classical Harmonic Oscillator Chain with an Impurity Mass. Journal of Physics A, 22, no. 8, pp. L331-L335.ADSGoogle Scholar
  83. Leibig, M. (1994) Model for the Propagation of Sound in Granular Materials. Phys. Rev. B, 49, no. 2, pp. 1647–1656.ADSGoogle Scholar
  84. Liu, C.-H., and Nagel, S.R. (1992) Sound in Sand. Phys. Rev. Letters, 68, no. 15, pp. 2301–2304.ADSGoogle Scholar
  85. Liu, C.-H., and Nagel S.R., (1993a) Sound in a Granular Material, Disorder and Nonlinearity. Phys. Rev. B, 48, no. 21, pp. 15646–15650.ADSGoogle Scholar
  86. Liu, C.-H., and Nagel, S.R. (1993b) Sound and Vibration in Granular Material. J. Phys.: Condens. Matter, 6, pp. A433-A436.ADSGoogle Scholar
  87. Liu, C.-H., Nagel, S.R., Schecter, D.A., Coppersmith, S.N., Majumdar, S., Narayan, O., and Witten, T.A. (1995) Force Fluctuations in Bead Packs. Science, 269, pp. 513–515.ADSGoogle Scholar
  88. Mach, E. (1868) Sitzungsber. math.-naturwiss. Cl. kaiserlich. Akad. Wissenschaften, Vienna, 57, no. 2, pp. 11–19.Google Scholar
  89. MacKay, R.S. (1999) Solitary Waves in a Chain of Beads under Hertz Contact. Physics Letters A, 251, no. 3, pp. 191–192.ADSGoogle Scholar
  90. Madsen, O.S., and Mei, C.C. (1969) The Transformation of a Solitary Wave over an Uneven Bottom. J. Fluid Mech., 39, pp. 781–791.ADSGoogle Scholar
  91. Manciu, F.S., Manciu, M., and Sen, S. (2000) Possibility of Controlled Ejection of Ferrofluid Grtains from a Magnetically Ordered Ferrofluid Using High Frequency Non-linear Acoustic Pulses — a Particle Dynamical Study. J. Magnetism and Magnetic Materials, 220, no. 2–3, pp. 285–292.Google Scholar
  92. Manciu, M., Sen, S., and Hurd, A.J. (1999a) The Propagation and Backscattering of Soliton-Like Pulses in a Chain of Quartz Beads and Related Problems (I). Propagation. Physica A, 274, pp. 588–606.ADSGoogle Scholar
  93. Manciu, M., Sen, S., and Hurd, A.J. (1999b) The Propagation and Backscattering of Soliton-Like Pulses in a Chain of Quartz Beads and Related Problems. (II). Backscattering Physica A, 214, pp. 607–618.ADSGoogle Scholar
  94. Manvi, R., Duvall, G.E., and Lowell, S.C. (1969) Finite Amplitude Longitudinal Waves in Lattice. Int. J. Mech. Sci., 11, pp. 1–9.zbMATHGoogle Scholar
  95. McCarthy, M.F. (1975) Singular Surfaces and Waves, in Continuum Physics (Edited by A.C. Eringen), vol. II. Academic Press, New York, pp. 450–521.Google Scholar
  96. Mehrabadi, M.M., and Nemat-Nasser, S. (1983) Stress, Dilatancy and Fabric in Granular Materials. Mechanics of Materials, 2, no. 2, pp. 155–61.Google Scholar
  97. Melin, S. (1994) Wave Propagation in Granular Assemblies. Phys. Rev. B, 49, no. 3, pp. 2353–2361.ADSGoogle Scholar
  98. Menon, V.V., Sharma, V.D., and Jeffrey, A. (1983) On the General Behavior of Acceleration Waves. Applicable Analysis, 16, pp. 101–120.MathSciNetzbMATHGoogle Scholar
  99. Mertens, F.G., and Buttner, H. (1986) Solitons on the Toda Lattice: Thermodynamical and Quantum-Mechanical Aspects. In: Solitons, (Edited by S.E. Trullinger, V.E. Zakharov, and V.L. Pokrovsky). Elsevier Science, New York, pp. 723–781.Google Scholar
  100. Mokross, F., and Buttner H. (1981) Comments on the Diatomic Toda Lattice. Phys. Rev. A24, no. 5, pp. 2826–2828.MathSciNetADSGoogle Scholar
  101. Naughton, M.J., Shelton, R., Sen, S., Manciu, M. (1998) Detection of Non-Metallic Landmines Using Shock Impulses and MEMS Sensors. In: Second International Conference on Detection of Abandoned Land Mines (IEE Conf. Publ. No. 458), (Second International Conference on Detection of Abandoned Land Mines, Edinburgh, 12–14 October 1998). IEE, London, pp. 249–252.Google Scholar
  102. Negreskul, S.I. (1993) Modeling of Granular Materials under Dynamic Loading. Author’s Abstract of PhD Thesis. Institute of Physics of Strength and Material Science, Tomsk, p. 17.Google Scholar
  103. Nesterenko, V.F. (1983a) Propagation of Nonlinear Compression Pulses in Granular Media. (Abstract of presentation on theoretical seminar of academician L.V. Ovsyannikov, 24 March, 1982). Izvestia Akademii Nauk SSSR, Mekhanika Gzidkosti i Gasa, no. 1, p. 191 (in Russian).Google Scholar
  104. Nesterenko, V.F. (1983b) Propagation of Nonlinear Compression Pulses in Granular Media. Prikl. Mekh. Tekh. Fiz., 24, no. 5, pp. 136–148 (in Russian). English translation: Journal of Applied Mechanics and Technical Physics (JAM), 1983b, no. 5, pp. 733–743.Google Scholar
  105. Nesterenko, V.F., Fomin V.M., and Cheskidov P.A. (1983a) Attenuation of Strong Shock Waves in Laminate Materials. In: Nonlinear Deformation Waves (Edited by U. Nigul and J. Engelbrecht). Springer-Verlag, Berlin, pp. 191–197.Google Scholar
  106. Nesterenko, V.F., Fomin, V.M., and Cheskidov P.A. (1983b) Damping of Strong Shocks in Laminar Materials. Zhurnal Prikladnoi Mekhaniki i Tehknicheskoi Fiziki, 24, no. 4, pp. 130–139 (in Russian). English translation: Journal of Applied Mechanics and Technical Physics, January 1984, pp. 567–575.Google Scholar
  107. Nesterenko, V.F., et al. (1986) Development of Protection Method for Reinforced Concrete Plates Against Spall after Contact Explosion. Technical Report, Special Design Office of High-Rate Hydrodynamics, Novosibirsk, #GR01850066141 (#SKB02870009933), p. 61.Google Scholar
  108. Nesterenko, V.F., and Lazaridi, A.N. (1987) Solitons and Shock Waves in One-Dimensional Granular Media. In: Problems of Nonlinear Acoustics, Proceedings of 11 International Symposium on Nonlinear Acoustics, Novosibirsk, 24–28 August, Part 1, pp. 309–313 (in Russian).Google Scholar
  109. Nesterenko, V.F. (1988) Nonlinear Phenomena under Impulse Loading of Heterogeneous Condensed Media. Doctor in Physics and Mathematics Thesis, Academy of Sciences, Siberian Branch, Russia, Lavrentyev Institute of Hydrodynamics, Novosibirsk.Google Scholar
  110. Nesterenko, V.F., and Lazaridi, A.N. (1990) The Peculiarities of Wave Processes in Periodical Systems of Particles with Different Masses. In: Obrabotka materialov impulsnymi nagruzkami, Novosibirsk, pp. 30–42 (in Russian).Google Scholar
  111. Nesterenko, V.F. (1992a) Nonlinear Waves in “Sonic Vacuum”. Fizika Goreniya i Vzryva, 28, no. 3 pp. 121–123 (in Russian).Google Scholar
  112. Nesterenko, V.F. (1992b) Pulse Compression Nature in Strongly Nonlinear Medium. In: Proc. of Second Intern. Symp. on Intense Dynamic Loading and Its Effects, Chengdu, China, pp. 236–240.Google Scholar
  113. Nesterenko, V.F. (1992c) A New Type of Collective Excitations in a “Sonic Vacuum.” Akustika neodnorodnykh sred, Novosibirsk, pp. 228–233 (in Russian).Google Scholar
  114. Nesterenko, V.F. (1992d) High-Rate Deformation of Heterogeneous Materials. Nauka, Novosibirsk, Ch. 2, pp. 51–80 (in Russian).Google Scholar
  115. Nesterenko, V.F. (1993a) Examples of “Sonic Vacuum,” Fizika Goreniya i Vzryva, no. 2, pp. 132–134 (in Russian).Google Scholar
  116. Nesterenko, V.F. (1993b) Solitary Waves in Discrete Medium with Anomalous Compressibility. Fizika Goreniya i Vzryva, 29, no. 2, pp. 134–136 (in Russian).MathSciNetGoogle Scholar
  117. Nesterenko, V.F., (1994) Solitary Waves in Discrete Media with Anomalous Compressibility and Similar to “Sonic Vacuum,” Journal De Physique IV, Colloque C8, supplement au Journal de Physique III, 4, pp. C8–72-C8–734.Google Scholar
  118. Nesterenko, V.F. (1995) Continuous Approximation for Wave Perturbations in a Nonlinear Discrete Medium. Fizika Goreniya i Vzyva, 31, no. 1, pp. 119–123 (in Russian). English translation: Explosion, Combustion and Shock Waves, July, 1995, pp. 116–119.Google Scholar
  119. Nesterenko, V.F., Lazaridi, A.N., and Sibiryakov, E.B. (1995) The Decay of Soliton at the Contact of Two “Acoustic Vacuums.” Prikl. Mekh. Tekh. Fiz., 36, no. 2, pp. 19–22 (in Russian). English translation: Journal of Applied Mechanics and Technical Physics (JAM), September, 1995, pp. 166–168.Google Scholar
  120. Nesterenko, V.F. (1999) Solitons, Shock Waves in Strongly Nonlinear Particulate Media. Presentation at 11th APS Topical Group Meeting on Shock Compression of Condensed Matter, Snowbird, Utah, 27 June-2 July 1999. Bulletin of the American Physical Society, 44, no. 2, p. 86.Google Scholar
  121. Nesterenko, V.F. (2000) Solitons, Shock Waves in Strongly Nonlinear Particulate Media. In: Shock Compression of Condensed Matter—1999 (Edited by M.D. Furnish, L.C. Chabildas, and R.S. Hixson). AIP, New York, pp. 177–180.Google Scholar
  122. Nesterenko, V.F. (2001) New Wave Dynamics in Granular State. In: Granular State, Materials Research Society Symposium Proceedings (Edited by S. Sen and M.L. Hunt). Materials Research Society, Warrendale, Pennsylvania, pp. BB3.1.1-BB.3.1.12.Google Scholar
  123. Nowacki, W.K. (1978) Stress Waves in Non-Elastic Solids. Pergamon Press. Oxford.Google Scholar
  124. Nunziato, J., and Walsh, E. (1977) On the Influence of Void Compaction and Non-Uniformity on the Propagation of One-Dimensional Acceleration Waves in Granular Materials. Arch. Rational Mech. Anal, 64, pp. 299–316.MathSciNetADSzbMATHGoogle Scholar
  125. Nunziato, J., and Cowin, S.C. (1979) A Nonlinear Theory of Elastic Materials with Voids. Arch. Rational Mech. Anal, 72, pp. 175–201.MathSciNetADSzbMATHGoogle Scholar
  126. Nunziato, J., Kennedy, J.E., and Walsh, E. (1978) The Behavior of One-Dimensional Acceleration Waves in Inhomogeneous Granular Solids. Int. J. Engng. Sci., 16, pp. 637–648.zbMATHGoogle Scholar
  127. Ono, H. (1972) Wave Propagation in an Inhomogeneous Anharmonic Lattice. Journal of the Physical Society of Japan, 32, no. 2, pp. 332–336.ADSGoogle Scholar
  128. Ostoja-Starzewski, M. (1984) Stress Wave Propagation in Discrete Random Solids. In: Wave Phenomena: Modern Theory and Applications (Edited by C. Rogers and T. Bryant). Elsevier Science, Amsterdam. North-Holland Mathematics Studies, vol. 97, pp. 267–278.Google Scholar
  129. Ostoja-Starzewski, M. (1991a) Wavefront Propagation in a Class of Random Microstructures—I: Bilinear Elastic Grains. Int. Journal of Non-Linear Mechanic, 26, pp. 659–669.ADSGoogle Scholar
  130. Ostoja-Starzewski, M. (1991b) Transient Waves in a Class of Random Heterogeneous Media. Appl. Mech. Rev. 44, no. 11, Part 2, pp. S199-S209.MathSciNetADSGoogle Scholar
  131. Ostoja-Starzewski, M. (1993) On the Critical Amplitudes of Acceleration Wave to Shock Wave Transition in White-Noise Random Media. J. Appl. Phys. (TAMP), 4, pp. 865–879.MathSciNetGoogle Scholar
  132. Ostoja-Starzewski, M. (1994) Transition of Acceleration Waves into Shock Waves in Random Media. Appl. Mech. Rev. (Special Issue: Nonlinear Waves in Solids), 47 (Pt. 2).Google Scholar
  133. Ostoja-Starzewski, M. (1995) Wavefront Propagation in a Class of Random Microstructures—II: Nonlinear Elastic Grains. Int. Journal of Non-Linear Mechanics, 30, no. 6, pp. 771–781.ADSzbMATHGoogle Scholar
  134. Parker, D.F., and Seymour, B.R. (1980) Finite Amplitude One-Dimensional Pulses in an Inhomogeneous Granular Material. Archive for Rational Mechanics and Analysis, 72, pp. 265–284.MathSciNetADSzbMATHGoogle Scholar
  135. Pendry, J.B., Holden, A.J., Robbins, D.J., and Stewart, W.J. (1999) Magnetism From Conductors and Enhanced Nonlinear Phenomena. IEEE Transactions on Microwave Theory and Techniques, 47, no. 11, pp. 2075–2084.ADSGoogle Scholar
  136. Radjai, F., Jean, M., Moreau, J.-J., Roux, S. (1996) Force Distribution in Dense Two-Dimensional Granular Systems. Phys. Rev. Letters, 77, no. 2, pp. 274–277.ADSGoogle Scholar
  137. Reddy, T.Y., Reid, S.R., and Barr, R. (1991) Experimental Investigation of Inertia Effects in One-Dimensional Metal Ring Systems Subjected to End Impact—II. Free-Ended Systems. Int. J. Impact Engng. 11, no. 4, pp. 463–480.Google Scholar
  138. Remoissenet, M. (1999) Waves Called Solitons (Concepts and Experiments). 3rd revised and enlarged edition. Springer-Verlag, Berlin.Google Scholar
  139. Rosenau, P. (1986a) A Quasi-Continuous Description of a Nonlinear Transmission Line. Physica Scripta, 34, pp. 827 – 829.ADSGoogle Scholar
  140. Rosenau, P. (1986b) Dynamics of Nonlinear Mass-Spring Chains Near the Continuum Limit. Physica Letters A, 118, no. 5, pp. 222–227.MathSciNetADSGoogle Scholar
  141. Rosenau, P. (1988) Dynamics of Dense Discrete Systems. Progress of Theoretical Physics, 79, no. 5, pp. 1028–1042.ADSGoogle Scholar
  142. Rosenau, P., and Hyman, J.M. (1993) Compactons: Solitons with Finite Wavelength. Physical Review Letters, 70, no. 5, pp. 564–567.ADSzbMATHGoogle Scholar
  143. Rosenau, P. (1994) Nonlinear Dispersion and Compact Structures. Physical Review Letters, 73, no. 13, pp. 1737–1741.MathSciNetADSzbMATHGoogle Scholar
  144. Rosenau, P. (1996) On Solitons, Compactons, and Lagrange Maps. Physical Letters A, 211, pp. 265–275.MathSciNetADSzbMATHGoogle Scholar
  145. Rosenau, P. (1997) On Nonanalytic Solitary Waves Formed by a Nonlinear Dispersion. Physics Letters, 230, nos. 5–6, pp. 305–318.Google Scholar
  146. Rossmanith, H.P., and Shukla, A. (1982) Photoelastic Investigation of Dynamic Load Transfer in Granular Media. Acta Mechanica, 42, pp. 211–225.Google Scholar
  147. Russel, J.S. (1838) Report of the Committee on Waves. Report of the 7th Meeting of the British Association for the Advancement of Science, Liverpool, pp. 417–496.Google Scholar
  148. Russel, J.S. (1845) On Waves. Report of the 14th Meeting of the British Association for the Advancement of Science, York, pp. 311–390.Google Scholar
  149. Sadd, M.H., Tai, QiMing, and Shukla, A. (1993) Contact Law Effects on Wave Propagation in Particulate Materials Using Distinct Element Modeling. Int. J. Non-Linear Mechanics, 28, no. 2, pp. 251–265.ADSzbMATHGoogle Scholar
  150. Samsonov, A.M. (1987) Transonic and Subsonic Localized Waves in Nonlinear Elastic Waveguide. In: Proc. of Intern. Conference on Plasma Physics, Naukova Dumka, Kiev, 4, pp. 88–90.Google Scholar
  151. Sander J., and Hutter, K. (1991) On the Development of the Theory of the Solitary Wave. A Historical Essay. Acta Mechanica, 86, pp. 111–152.MathSciNetzbMATHGoogle Scholar
  152. Sander, J., and Hutter K. (1992) Evolution of Weakly Non-Linear Shallow Water Waves Generated by a Moving Boundary. Acta Mechanica, 91, pp. 19–155.Google Scholar
  153. Scott, D.R., and Stevenson, DJ. (1984) Magma Solitons. Geophysical Research Letters, 11, no. 11, pp. 1161–1164.ADSGoogle Scholar
  154. Sen, S., Manciu, M., and Wright, J.D. (1998) Solitonlike Pulses in Perturbed and Driven Hertzian Chains and Their Possible Applications in Detecting Buried Impurities. Phys. Rev., E, 57, no. 2, pp. 2386–2397.ADSGoogle Scholar
  155. Sen, S. (1998) Soliton-like Objects in Granular Beds. Presentation at UCSD Seminar in Mechanical and Materials Engineering, December 16, 1998.Google Scholar
  156. Sen, S., Manciu, M., and Manciu, F.S. (1999) Ejection of Ferrofluid Grains Using Nonlinear Acoustic Impulses—A Particle Dynamical Study. Applied Physics Letters, 75, no. 10, pp. 1479–1481.ADSGoogle Scholar
  157. Sen, S., and Manciu, M. (1999) Discrete Hertzian Chains and Solitons. Physica A, 268, pp. 644–649.Google Scholar
  158. Shukla, A., Sadd, M.H., Xu, Y., and Tai, Q.M. (1993) Influence of Loading PulseDuration on Dynamic Load Transfer in a Simulated Granular Medium. J. Mech. Solids, J. Mech. Solids, 41, no. 11, pp. 1795–1808.ADSGoogle Scholar
  159. Singh, R., Shukla, A., and Zervas, H. (1996) Explosively Generated Pulse Propagation through Particles Containing Natural Cracks. Mechanics of Materials, 23, pp. 255–270.Google Scholar
  160. Sinkovits, R.S., and Sen, S. (1995) Nonlinear Dynamics in Granular Columns. Phys. Rev. Letters, 74, no. 14, pp. 2686–2689.ADSGoogle Scholar
  161. Sinkovits, R.S., and Sen, S. (1996) Sound Propagation in Impure Granular Columns. Phys. Rev., E, 54, no. 6, pp. 6857–6865.ADSGoogle Scholar
  162. Smith, D.R., Vier, D.C., Padilla, W., Nemat-Nasser, S.C., and Schultz, S. (1999) Loop-Wire Medium for Investigating Plasmons at Microwave Frequencies. Applied Physics Letters, 75, no. 10, pp. 1425–1427.ADSGoogle Scholar
  163. Sobczyk, K. (1992) Korteweg-de Vries Solitons in a Randomly Varying Medium. Int. Journal of Non-Linear Mechanics, 27, no. 1, pp. 1–8.MathSciNetADSzbMATHGoogle Scholar
  164. Strenzwik, D.E. (1979) Shock Profiles Caused by Different End Conditions in One-Dimensional Quiscent Lattices, J. Appl. Physics, 50, no. 11, pp. 6767–6772.ADSGoogle Scholar
  165. Takahashi, D., and Satsuma, J. (1988) Explicit Solutions of Magma Equation. J. Phys. Soc. Japan, 57, no. 2, pp. 411–421.MathSciNetADSGoogle Scholar
  166. Takahashi, D., Sachs, J.R., and Satsuma, J. (1990) Soliton Phenomena in a Porous Medium. In: Research Reports in Physics, Nonlinear Physics (Edited by Gu Chaohao, Li Yishen, and Tu Guizhang). Springer-Verlag, Berlin, pp. 214–220.Google Scholar
  167. Takahashi, D., and Sato, Y. (1949) On the Theory of Elastic Waves in a Granular Substance. Bulletin of the Earthquake Research Institute, Japan, 27, pp. 11–16.MathSciNetGoogle Scholar
  168. Takahashi, D., and Sato, Y. (1950) On the Theory of Elastic Waves in a Granular Substance. Bulletin of the Earthquake Research Institute, Japan, 28, pp. 37–43.MathSciNetGoogle Scholar
  169. Thornton, C, and Barnes, D.J. (1986) Computer Simulated Deformation of Compact Granular Assemblies. Acta Mechanica, 64, pp. 45–61.Google Scholar
  170. Timoshenko, S.P., and Goodier J.N. (1987) Theory of Elasticity, 3rd ed. McGraw-Hill, New York, p. 414.Google Scholar
  171. Toda, M. (1981) Theory of Nonlinear Lattices. Springer Series in Solid State Science, Vol. 20, Springer-Verlag, Berlin.zbMATHGoogle Scholar
  172. Travers, T., Ammi, M., Bideau, D., Gervois, A., Messager, J.C., and Troadec, J.P. (1987) Uniaxial Compression of 2-D Packings of Cylinders. Effects of Weak Disorder. Europhys. Letters, 4, no. 3, pp. 329–332.ADSGoogle Scholar
  173. Travers, T., Ammi, M., Bideau, D., Gervois, A., Messager, J.C., and Troadec, J.P. (1988) Mechanical Size Effects in 2-D Granular Media. J. Phys. France, 49, pp. 939–948.Google Scholar
  174. Triantafyllidis, N., and Bardenhagen, S. (1993) On High Order Gradient Continuum Theories in 1-D Nonlinear Elasticity. Derivation from and Comparison to the Corresponding Discrete Models. Journal of Elasticity, 33, pp. 259–293.MathSciNetzbMATHGoogle Scholar
  175. Tsai, D.H., and Beckett, C.W. (1966) Shock Wave Propagation in Cubic Lattices. Journal of Geophysical Research, 71, no. 10, pp. 2601–2608.ADSGoogle Scholar
  176. Tsemahovich, B.D. (1988) Concept of Support Selection for Explosive Welding. Proc. International Symposium on Metal Explosive Working, Purdubice, Chehoslovakia, Vol. 1, pp. 82–89 (in Russian).Google Scholar
  177. Walton, K. (1987) The Effective Elastic Moduli of a Random Packing of Spheres. J. Mech. Phys. Solids, 35, no. 2, pp. 213–226.ADSzbMATHGoogle Scholar
  178. Whitham, G.B. (1970) Two-Timing, Variational Principles and Waves. J. Fluid Mechanics,44, pp. 373–395.MathSciNetADSzbMATHGoogle Scholar
  179. Whitham, G.B. (1974) Linear and Nonlinear Waves. Wiley, New York.zbMATHGoogle Scholar
  180. Wright, T.W. (1984) Weak Shocks and Steady Waves in a Nonlinear Elastic Rod or Granular Material. Int. J. Solids Structures, 20, nos. 9/10, pp. 911–919.Google Scholar
  181. Wright, T.W. (1985) Nonlinear Waves in a Rod: Results for Incompressible Elastic Materials. Studies in Applied Mathematics, 72, pp. 149–160.MathSciNetzbMATHGoogle Scholar
  182. Yablonovitch, E. (1993) Photonic Band-Gap Crystals. J. Phys.: Condens. Matter, 5, pp. 2443–2460.ADSGoogle Scholar
  183. Zabusky, N.J., and Galvin, C.J. (1971) Shallow-Water Waves, the Korteveg-de Vries Equation and Solitons. J. Fluid Mech., 47, pp. 811–824.ADSGoogle Scholar
  184. Zaikin, A.D. (1990) Effective Elastic Moduli of Granular Media. Prikl. Mekh. Tekh. Fiz., 31, no. 1, pp. 91–96 (in Russian). English translation: Journal of Applied Mechanics and Technical Physics(JAM), July, 1990, pp. 85–89.Google Scholar
  185. Zakharov, V.E. (1972) Collapse of Langmuir Waves. Sov. Phys. JETP, 35, no. 5, pp. 908–914.ADSGoogle Scholar
  186. Zakharov, V. E. (1974) On Stochastization of One-Dimensional Chains of Nonlinear Oscillators. Sov. Phys. JETP, 38, no. 1, pp. 108–110.ADSGoogle Scholar
  187. Zhu, Y., Shukla, A., and Sadd, M.H. (1996) The Effect of Microstructural Fabric on Dynamic Load Transfer in Two-Dimensional Assemblies of Elliptical Particles. J. Mech. Phys. Solids, 44, no. 8, pp. 1283–1303.ADSGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Vitali F. Nesterenko
    • 1
  1. 1.Department of Mechanical and Aerospace EngineeringUniversity of California at San DiegoLa JollaUSA

Personalised recommendations