Differential Conservation Equations and Time-Dependent Flow

  • Jerry W. Forbes
Part of the Shock Wave and High Pressure Phenomena book series (SHOCKWAVE)


Much of the shock field was developed on the study of materials such as metals that are in equilibrium under shock loading. The invention of improved diagnostics such as laser interferometers led to measurement of shock wave profiles that showed time dependence for some materials. In order to understand the treatment of time-dependent flow requires solving the differential conservation equations along with a materials constitutive equation. Numerical solutions of these equations may be required to describe a materials behavior under dynamic loading. These equations and there application are the subject of this and following chapters.


Shock Wave Shock Front Peak Particle Velocity Hugoniot Elastic Limit Elastic Precursor 
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.


  1. 1.
    J.C. Jaeger, Elasticity, Fracture and Flow: With Engineering and Geological Applications. Science Paperbacks, 1969Google Scholar
  2. 2.
    W. Band, G.E. Duvall, Physical nature of shock propagation. Am. J. Phys. 20, 780 (1961)CrossRefGoogle Scholar
  3. 3.
    J.W. Swegle, D.E. Grady, Shock viscosity and the prediction of shock wave rise times. J. Appl. Phys 58, 692 (1985)CrossRefGoogle Scholar
  4. 4.
    L.M. Barker, R.E. Hollenbach, Shock-wave studies of PMMA, fused silica, and sapphire. J. Appl. Phys. 41(10), 4208–4226 (1970)CrossRefGoogle Scholar
  5. 5.
    T.P. Liddiard Jr., The compression of polymethyl methacrylate by low amplitude shock waves. in Proceedings of Fourth Symposium (International) on Detonation, White Oak, 12–15 Oct 1965Google Scholar
  6. 6.
    D.N. Schmidt, M.W. Evans, Nature 206, 1348 (1965)CrossRefGoogle Scholar
  7. 7.
    Y.M. Gupta, Determination of the impact response of PMMA using combined compression and shear loading. J. Appl. Phys. 51(10), 5352 (1980)CrossRefGoogle Scholar
  8. 8.
    K.W. Schuler, Propagation of steady shock waves in polymethyl methacrylate. J. Mech. Phys. Solid. 18, 277 (1970)CrossRefGoogle Scholar
  9. 9.
    J.W. Nunziato, K.W. Schuler, E.K. Walsh, The bulk response of viscoelastic solids. Trans. Soc. Rheol. Wiley, 16(1) 15–32 (1972)Google Scholar
  10. 10.
    G.E. Duvall, Shock waves in condensed media. in Proceedings of the International School of Physics “Enrico Fermi” ed. by P. Caldiorola, H. Knoepfel, (Academic, 1971), pp. 7–50Google Scholar
  11. 11.
    G.E. Duvall, The shocked piezoelectric disk as a Maxwell solid. J. Appl. Phys. 48(10), 4415 (1977)CrossRefGoogle Scholar
  12. 12.
    J.W. Forbes, Experimental investigation of the kinetics of the shock-induced phase transformation in Armco iron. Ph.D. thesis, WSU, 1976Google Scholar
  13. 13.
    J.W. Forbes, Experimental investigation of the kinetics of the shock-induced phase transformation in Armco iron. NSWC TR 77–137, 15, Dec 1977 (Unpublished)Google Scholar
  14. 14.
    L.M. Barker, R.E. Hollenbach, Shock wave study of the α↔ε phase transtion in iron. J. Appl. Phys. 45(11), 4872 (1974)CrossRefGoogle Scholar
  15. 15.
    D.B. Hayes, Polymorphic phase transformation rates in shock-loaded potassium chloride. J. Appl. Phys. 45(3), 1208 (1974)CrossRefGoogle Scholar
  16. 16.
    G.E. Duvall, Maxwell-like relations in condensed materials decay of shock waves. Iran. J. Sci. Technol. 7, 57 (1978)Google Scholar
  17. 17.
    J.R. Asay et al., Effects of point defects on elastic-precursor decay in LiF. J. Appl. Phys. 43, 2132 (1972)CrossRefGoogle Scholar
  18. 18.
    Y.M. Gupta, Stress dependence of elastic wave attenuation in LiF. J. Appl. Phys. 46, 3395 (1975)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Energetics Technology CenterSt. CharlesUSA

Personalised recommendations