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Traditional Analysis of Nonlinear Wave Propagation in Solids

  • Lee Davison
Chapter
Part of the Shock Wave and High Pressure Phenomena book series (SHOCKWAVE)

Abstract

Before beginning a formal discussion of nonlinear wave propagation, it seems useful to describe some of the basic observations. Most of the work that has been done concerns the response of materials to compression because the experiments are convenient and permit access to states of larger deformation than can be attained in materials under tension. The simplest situation considered is that in which a wave is introduced into the material by applying a compressive force uniformly over the surface of a halfspace. When this force increases smoothly in time, the resulting wave is also smooth. However, it is observed that (with a few exceptions) the gradient in such a wave increases with increasing propagation distance. Eventually, the wavefront evolves into an almost discontinuous jump. One cannot expect formation of a true discontinuity, but this is often a useful mathematical approximation to reality.

Keywords

Shock Compression Jump Condition Detonation Product Uniaxial Strain Traditional Analysis 
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.

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References

  1. [1]
    J.N. Johnson and R. Chéret (eds.), Classic Papers in Shock Compression Science, Springer, New York (1998).zbMATHGoogle Scholar
  2. [2]
    R. Courant and K.O. Friedrichs, Supersonic Flow and Shock Waves, Interscience, New York (1948).zbMATHGoogle Scholar
  3. [3]
    V.F. Nesterenko, iDynamics of Heterogeneous Materials, Springer-Verlag, New York (2001).CrossRefGoogle Scholar
  4. [4]
    C. Truesdell and R.A. Toupin, The Classical Field Theories, in Handbuch der Physik III/1 (ed. S. Flügge), Springer-Verlag, Berlin (1960).Google Scholar
  5. [5]
    L.E. Malvern, Introduction to the Mechanics of Continuous Media, Prentice-Hall, Englewood Cliffs, NJ (1969).Google Scholar
  6. [6]
    D.S. Drumheller, Introduction to Wave Propagation in Nonlinear Fluids and Solids, Cambridge University Press, Cambridge (1998).CrossRefGoogle Scholar
  7. [7]
    C. Truesdell and W. Noll, in Handbuch der Physik III/3 (ed. S. Flügge), Springer-Verlag, Berlin (1965).Google Scholar
  8. [8]
    M.H. Rice, R.G. McQueen, and J.M. Walsh, in Solid State Physics 6 (eds. F. Seitz and W. Turnbull), Academic Press, New York, pp. 1–63 (1958).Google Scholar
  9. [9]
    R.G. McQueen, S.P. Marsh, J.W. Taylor, J.N. Fritz, and W.J. Carter, in High Velocity Impact Phenomena (ed. R. Kinslow), Academic Press, New York, pp. 293–417 with appendices on pp. 515-568 (1970).CrossRefGoogle Scholar
  10. [10]
    R.N. Thurston, in Handbuch der Physik IVa/4 (ed. S. Flügge), Springer-Verlag, Berlin, pp. 109–308 (1974).Google Scholar
  11. [11]
    J.R. Asay and M. Shahinpoor, eds., High-Pressure Shock Compression of Solids, Springer-Verlag, New York (1993).Google Scholar
  12. [12]
    Shock compression of Condensed Matter — 2001 (eds. M.D. Furnish, N.N. Thadhani, and Y. Horie), American Institute of Physics, Melville, NY (2002).Google Scholar
  13. [13]
    Eleventh International Detonation Symposium, U.S. Office of Naval Research report ONR33300-5 (2000).Google Scholar
  14. [14]
    L.M. Barker, M. Shahinpoor, and L.C. Chhabildas, in [11], pp. 43–73.Google Scholar
  15. [15]
    L. Davison and M. Shahinpoor, eds., High-Pressure Shock Compression of Solids—III, Springer-Verlag, New York (1997).Google Scholar
  16. [16]
    S.K. Sikka, B.K. Godwal, and R. Chidambaram, in [15], pp. 1–35.Google Scholar
  17. [17]
    S. Minshall, J. Appl. Phys. 26, pp. 463–469 (1955).ADSCrossRefGoogle Scholar
  18. [18]
    J.W. Taylor, J. Appl. Phys. 34, pp. 2727–2731 (1963)ADSCrossRefGoogle Scholar
  19. [19]
    J.N. Johnson, in [11], pp. 217–264.Google Scholar
  20. [20]
    G.T. Gray III, in [11], pp. 187–215.Google Scholar
  21. [21]
    T. Mashimo, in [15], pp. 101–146.Google Scholar
  22. [22]
    J. Cagnoux and J.-Y. Tranchet, in [15], pp. 147–169.Google Scholar
  23. [23]
    J.W. Nunziato, E.K. Walsh, K.W. Schuler, and L.M. Barker, in Handbuch der Physik IVa/4 (ed. S. Flügge), Springer-Verlag, Berlin, pp. 1–108 (1974).Google Scholar
  24. [24]
    R.A. Graham, Solids Under High-Pressure Shock Compression, Springer-Verlag, New York (1993).Google Scholar
  25. [25]
    T.H. Antoun, L. Seaman, D.R. Curran, G.I. Kanel, S.V. Razorenov, and A.V. Utkin, Dynamic Fracture of Materials, Springer-Verlag, New York, in press.Google Scholar
  26. [26]
    L. Davison, D.E. Grady, and M. Shahinpoor, eds., High-Pressure Shock Compression of Solids—II: Dynamic Fracture and Fragmentation, Springer-Verlag, New York (1996).zbMATHGoogle Scholar
  27. [27]
    A.K. Zurek and M.A. Meyers, in [26], pp. 25–70.Google Scholar
  28. [28]
    L. Davison, Y. Horie, and M. Shahinpoor, eds., High-Pressure Shock Compression of Solids—IV: Response of Highly Porous Solids to Shock Loading, Springer-Verlag, New York (1997).Google Scholar
  29. [29]
    L.S. Belmett, K. Tanaka, and Y. Horie, in [28], pp. 105–175.Google Scholar
  30. [30]
    R. Engelke and S.A. Sheffield, in [15], pp. 171–239.Google Scholar
  31. [31]
    S.A. Sheffield, R.L. Gustavsen, and M.U. Anderson, in [28], pp. 23–61, (1997).Google Scholar
  32. [32]
    M.R. Baer in [28], pp. 63–82.Google Scholar
  33. [33]
    F.L. Addessio and J.B. Aidun, in [15], pp. 241–275.Google Scholar
  34. [34]
    T.J. Ahrens, in [11], pp. 75–113.Google Scholar
  35. [35]
    L. Davison, Y. Horie, and T. Sekine, eds., High-Pressure Shock Compression of Solids—V: Shock Chemistry with Application to Meteorite Impacts, Springer-Verlag, New York (2003).Google Scholar
  36. [36]
    N.N. Thadhani and T. Aizawa, in [28], pp. 257–287.Google Scholar
  37. [37]
    J.M. McGlaun and P. Yarrington, in [11], pp. 323–353.Google Scholar
  38. [38]
    J.R. Asay and G.I. Kerley, Int. J. Impact Engng. 5, pp. 69–99 (1987).CrossRefGoogle Scholar

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© Springer Science+Business Media New York 2003

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  • Lee Davison

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