Elastic-Plastic Waves in Porous Materials

  • V. M. Fomin
  • S. P. Kiselev
Part of the High-Pressure Shock Compression of Condensed Matter book series (SHOCKWAVE)


Consider an elastic-plastic material containing a great number of spherical voids. A precise solution of the problem of deformation of such a material is next to impossible. Therefore, various model approaches are widely used, as briefly discussed in Sec. 8.2. The authors’ mathematical model is presented in Sec. 8.3 and some of its mathematical and physical aspects are studied. Shock wave propagation in porous aluminum and iron is examined in Sec. 8.4 on the basis of the present model. In Sec. 8.5, an expansion shock wave in a porous elastic-plastic medium is theoretically predicted and investigated. Mathematical symbols used are listed and defined at the end of the chapter.


Shock Wave Porous Material Impact Velocity Yield Surface Expansion Wave 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    J. Thouvenin, J. Phys. 27, pp. 183–189 (1966).CrossRefGoogle Scholar
  2. [2]
    R. Hoffman, D.J. Andrews, and D.E. Maxwell, J. Appl. Phys. 39, pp. 4555–4562 (1968).ADSCrossRefGoogle Scholar
  3. [3]
    V.F. Nesterenko, Impulse Loading of Heterogeneous Materials, Nauka, Novosibirsk (1992) (in Russian).Google Scholar
  4. [4]
    V.F. Nesterenko, V.M. Fomin, and P.A. Cheskidov, in Numerical Methods for Elastic and Plastic Problems (ed. V.M. Fomin), ITAM SB RAS, Novosibirsk, pp. 231–236 (1988) (in Russian).Google Scholar
  5. [5]
    Ya.B.. Zel’dovich and Yu.P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena, Academic Press, New York (1967).Google Scholar
  6. [6]
    W. Herrmann, J. Appl. Phys. 40, pp. 2490–2499 (1969).ADSCrossRefGoogle Scholar
  7. [7]
    S.P. Kiselev, V.M. Fomin, and Yu.A. Shitov, Appl. Mech. Tech. Phys., pp. 100–104 (1990) (in Russian).Google Scholar
  8. [8]
    S.P. Kiselev, G.A. Ruev, A.P. Trunev, V.M. Fomin, and M.S. Shavaliev, Shock-Wave Processes in Two-Component and Two-Phase Media, Nauka, Novosibirsk (1992) (in Russian).Google Scholar
  9. [9]
    S.S. Grigoryan, Appl. Math. Mech. 24, pp. 1057–1072 (1960) (in Russian).Google Scholar
  10. [10]
    J.W. Swegle, J. Appl. Phys. 51, pp. 2574–2580 (1980).ADSCrossRefGoogle Scholar
  11. [11]
    A.A. Bakanova, I.P. Dudolatov, and Yu.N. Sutulov, Appl. Mech. Tech. Phys., pp. 117–122 (1974) (in Russian).Google Scholar
  12. [12]
    K.K. Krupnikov, M.I. Brazhnik, and V.P. Krupnikova, J. Exp. Theoret. Phys. 42, pp. 675–685 (1962) (in Russian).Google Scholar
  13. [13]
    M.M. Carroll and A.C. Holt, J. Appl. Phys. 43, pp. 1626–1635 (1972).ADSCrossRefGoogle Scholar
  14. [14]
    N.N. Belov, A.I. Korneev, and A.P. Nikolaev, Appl. Mech. Tech. Phys., pp. 132–136 (1985) (in Russian).Google Scholar
  15. [15]
    S.Z. Dunin and V.V. Surkov, Appl. Mech. Tech. Phys., p. 131 (1982) (in Russian).Google Scholar
  16. [16]
    A.V Attetkov, L.N. Vlasova, V.V. Selivanov, and V.S. Solov’ev, Appl. Mech. Tech. Phys., pp. 120–127 (1984) (in Russian).Google Scholar
  17. [17]
    J.D. Eshelby, Proc. Roy. Society A241, pp. 376–396 (1957).MathSciNetADSCrossRefGoogle Scholar
  18. [18]
    Z. Hashin, Trans. ASME E32, p. 630 (1965).Google Scholar
  19. [19]
    R. Hill, J. Mech. Phys. Solids 11, pp. 357–372 (1963).ADSzbMATHCrossRefGoogle Scholar
  20. [20]
    T.D. Shermergor, Theory of Microinhomogeneous Media, Nauka, Moscow (1977) (in Russian).Google Scholar
  21. [21]
    R.I. Nigmatulin, Fundamentals of Heterogeneous Media Mechanics, Nauka, Moscow (1978) (in Russian).Google Scholar
  22. [22]
    V.N. Nikolaevsky, K.S. Basniev, A.T. Gorbunov, and G.A. Zotov, Mechanics of Saturated Porous Media, Nedra, Moscow (1970) (in Russian).Google Scholar
  23. [23]
    A.L. Gurson, Trans. ASME, Series D, 99, p. 2 (1977).Google Scholar
  24. [24]
    S. Shima and M. Oyane, Int. J. Mech. Sci. 18, p. 285 (1976).CrossRefGoogle Scholar
  25. [25]
    O. Richmond and R.E. Smelser, Alcola Technical Center Memorandum (1985).Google Scholar
  26. [26]
    V. Tvergaard, Int. J. Solids Structures 25, p. 1143 (1989).CrossRefGoogle Scholar
  27. [27]
    A.L. Sadyrin, J. Phys. 4, p. 94 (1994).Google Scholar
  28. [28]
    V.A. Skreepnjak, Shock Waves in Condensed Matter, St. Petersburg (1994) (in Russian).Google Scholar
  29. [29]
    J.N. Johnson and F.L. Addessio, J. Appl. Phys. 64, pp. 6699–6712 (1988).ADSCrossRefGoogle Scholar
  30. [30]
    S.P. Kiselev, in Filtration of Multiphase System, Institute of Theoretical and Applied Mechanics of the Siberian Department of Sciences (ITPM SO AN), Novosibirsk, pp. 151–166 (1991) (in Russian).Google Scholar
  31. [31]
    S.P. Kiselev and V.M. Fomin, J. Theoret. Appl. Mech. 34, pp. 861–869 (1993) (translated from Russian).MathSciNetADSGoogle Scholar
  32. [32]
    S.P. Kiselev, Numerical Simulation of Elastic-Plastic Waves Propagation in Porous Material, Preprint ITAM SB RAS, Novosibirsk (1994) (in Russian).Google Scholar
  33. [33]
    S.P. Kiselev and V.M. Fomin, Model. Mech. 5, pp. 65–72 (1991) (in Russian).Google Scholar
  34. [34]
    V.M. Fomin and S.P. Kiselev, in Shock Waves 1 (ed. K. Takayama), Springer-Verlag, Berlin, pp. 373–379 (1991).Google Scholar
  35. [35]
    C.L. Horn and R.M. McMeeking, J. Appl. Mech. 56, p. 309 (1989).ADSCrossRefGoogle Scholar
  36. [36]
    M.L. Wilkins, in Computational Methods in Hydrodynamics, Mir, Moscow, pp. 212–263 (1967).Google Scholar
  37. [37]
    B.M. Butcher, M.M. Carroll, and A.C. Holt, J. Appl. Phys. 45, pp. 3864–3875 (1974).ADSCrossRefGoogle Scholar
  38. [38]
    CD. Lundergan and W. Herrmann, J. Appl. Phys. 34, pp. 2046–2052 (1963).ADSCrossRefGoogle Scholar
  39. [39]
    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 (1970).Google Scholar
  40. [40]
    L.M. Barker and R.E. Hollenbach, J. Appl. Phys. 41, pp. 4208–4226 (1970).ADSCrossRefGoogle Scholar
  41. [41]
    V.N. Aptukov, P.K. Nikolaev, and V.I. Romanchenko, Appl. Mech. Tech. Phys., pp. 92–98 (1988) (in Russian).Google Scholar
  42. [42]
    S.P. Kiselev, Appl. Mech. Tech. Phys., pp. 122–127 (1991) (in Russian).Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1997

Authors and Affiliations

  • V. M. Fomin
  • S. P. Kiselev

There are no affiliations available

Personalised recommendations