Shock Waves

, Volume 27, Issue 2, pp 291–297 | Cite as

Particle velocity non-uniformity and steady-wave propagation

  • Yu. I. MeshcheryakovEmail author
Original Article


A constitutive equation grounded in dislocation dynamics is shown to be incapable of describing the propagation of shock fronts in solids. Shock wave experiments and theoretical investigations motivate an additional collective mechanism of stress relaxation that should be incorporated into the model through the standard deviation of the particle velocity, which is found to be proportional to the strain rate. In this case, the governing equation system results in a second-order differential equation of square non-linearity. Solution to this equation and calculations for D16 aluminum alloy show a more precise coincidence of the theoretical and experimental velocity profiles.


Particle velocity Meso–macro momentum exchange Shock waves Dislocation dynamics 



The author thanks A.K. Divakov and Yu. A. Petrov for the velocity profiles used.


  1. 1.
    Johnson, J.N., Jones, O.E., Michaels, T.E.: Dislocation dynamics and single-crystal constitutive relations: shock-wave propagation and precursor decay. J. Appl. Phys. 41, 2230–2239 (1970)Google Scholar
  2. 2.
    Ashby, M.F.: The deformation of plastically non-homogeneous materials. Phil. Mag. 21, 399–424 (1970)CrossRefGoogle Scholar
  3. 3.
    Johnson, J.N., Barker, L.M.: Dislocation dynamics and steady plastic wave profiles in 6061-T6 aluminum. J. Appl. Phys. 40, 4321–4335 (1969)CrossRefGoogle Scholar
  4. 4.
    Prieto, F.E., Renero, C.: Steady shock profile in solids. J. Appl. Phys. 44, 4013–4019 (1973)CrossRefGoogle Scholar
  5. 5.
    Chhabildas, L.C., Asay, J.R.: Rise-time measurements of shock transitions in aluminum, copper, and steel. J. Appl. Phys. 50, 2749–2756 (1979)CrossRefGoogle Scholar
  6. 6.
    Grady, D.E., Kipp, M.E.: The growth of unstable thermoplastic shear with application to steady-wave shock compression of solids. J. Mech. Phys. Solids 35, 95–119 (1987)CrossRefzbMATHGoogle Scholar
  7. 7.
    Swegle, J.W., Grady, D.E.: Shock viscosity and the prediction of shock wave rise-times. J. Appl. Phys. 58, 692–701 (1985)CrossRefGoogle Scholar
  8. 8.
    Asay, J.R., Barker, L.M.: Interferometric measurements of shock-induced internal particle velocity and spatial variations of particle velocity. J. Appl. Phys. 45, 2540–2546 (1974)CrossRefGoogle Scholar
  9. 9.
    Lipkin, J., Asay, J.R.: Reshock and release of shock-compressed 6061–T6 aluminum. J. Appl. Phys. 48, 182–189 (1977)CrossRefGoogle Scholar
  10. 10.
    Meshcheryakov, Yu.I., Divakov, A.K., Zhigacheva, N.I., Makarevich, I.P., Barakhtin, B.K.: Dynamic structures in shock-loaded copper. Phys. Rev. B. 78, 064301–064316 (2008)Google Scholar
  11. 11.
    Meshcheryakov, Yu.I., Divakov, A.K., Zhigacheva, N.I., Barakhtin, B.K.: Regimes of interscale momentum exchange in shock deformed solids. Int. J. Impact Eng. 57, 99–107 (2013)Google Scholar
  12. 12.
    Taylor, J.W.: Dislocation dynamics and dynamic yielding. J. Appl. Phys. 36, 3146–3155 (1965)CrossRefGoogle Scholar
  13. 13.
    Johnston, W.G., Gilman, J.J.: Dislocation velocities, dislocation densities, and plastic flow in lithium fluoride crystals. J. Appl. Phys. 30, 129–144 (1959)CrossRefGoogle Scholar
  14. 14.
    Ferguson, W.G., Kumar, A., Dorn, J.E.: Dislocation damping in aluminum at high strain rates. J. Appl. Phys. 38, 1863–1869 (1967)CrossRefGoogle Scholar
  15. 15.
    Bland, D.R.: On shock structure in a solid. J. Inst. Math. Appl. 1, 56–75 (1965)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Arvidsson, N.E., Gupta, Y.M., Duvall, G.E.: Precursor decay in 1060 aluminum. J. Appl. Phys. 46, 447–457 (1975)Google Scholar
  17. 17.
    Yano, K., Horie, Y.: Discrete-element modeling of shock compression of polycrystalline copper. Phys. Rev. B. 59, 13672–13680 (1999)CrossRefGoogle Scholar
  18. 18.
    Case, S., Horie, Y.: Discrete element simulation of shock wave propagation in polycrystalline copper. J. Mech. Phys. Solids 55, 589–614 (2007)CrossRefzbMATHGoogle Scholar
  19. 19.
    Hinze, J.O.: Turbulence. McGraw-Hill, New York (1959)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Institute of Problems of Mechanical Engineering, Russian Academy of SciencesSaint-PetersburgRussia

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