Modeling Penetration Phenomena

  • J. Buchar
  • J. Hřebíček


Penetration phenomena are of interest in numerous areas (cf. [3]). They are often associated with the problem of nuclear waste containment and with the protection of spacecraft or satellites from debris and/or meteorite impact. Formally the penetration is defined as the entrance of a projectile into the target without completing its passage through the body. The penetration phenomenon can be characterized according to the impact angle, the geometry and material characteristics of the target and the projectile and the striking velocity. In this chapter we limit our considerations to the normal incidence impact of a long rod on a semi-infinite target. This model corresponds for example to the situation in which a very thick armor is penetrated by a high kinetic energy projectile. The most efficient method for the solution of this problem is the numerical modeling by the finite elements method. Many finite elements computer programs are capable of handling very complex material constitutive relations. These programs are expensive and often require a substantial amount of execution time. This is the main reason why simple one-dimensional theories still have considerable value. Such theories also provide insight into the interactions between the physical parameters and their relationship to the outcome of the event. These interactions are usually difficult to ascertain from the computer analyses mentioned above. As a result, simple theories often provide the basis for the design of experiments, refining the areas in which numerical modeling by finite elements methods is applied. In this spirit, we will investigate some penetration models which are treated using Maple.


Target Strength Ballistic Experiment Penetration Velocity Target Resistance Penetration Path 
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]
    V. P. Alekseevskii, Penetration of a rod into a target at high velocity, Combustion, explosion and shock waves, 2, 1966, pp. 63–66.CrossRefGoogle Scholar
  2. [2]
    C. E. Anderson Jr., S. R, Bodner, Ballistic impact: the status of analytical and numerical modeling, Int. J. Impact Engng., 7, 1988, pp. 9–35.CrossRefGoogle Scholar
  3. [3]
    Z. BÍlek and J. Buchar, The behavior of metals under high rates of strain (in Czech), Academia, Praha, 1984.Google Scholar
  4. [4]
    J. Buchar, M. Lazar, S. Rolc, On the penetration of steel targets by long rods, Acta Techn. CSAV 39, 1994, pp. 193–220.Google Scholar
  5. [5]
    D. R. Christman, J. W. Gehring, Analysis of high-velocity projectile penetration mechanics, J. Appl. Phys., 27, 1966, pp. 63–68.Google Scholar
  6. [6]
    J. D. Cinnamon et al., A one — dimensional analysis of rod penetration, Int. J. Impact Engng., 12, pp. 145–166, 1992.CrossRefGoogle Scholar
  7. [7]
    J.Dehn, A unified theory of penetration, Int. J. Impact Engng., 5, 1987, pp. 239–248.CrossRefGoogle Scholar
  8. [8]
    W. Herrmann, J. S. Wilbeck, Review of hypervelocity penetration theories, Int. J. Impact Engng., 5, 1987, pp. 307–322,CrossRefGoogle Scholar
  9. [9]
    V. K. Luk, M. J. Forrestal, D.E. Amos, Dynamical spherical cavityexpansion of strain-hardening materials, J. Appl. Phys., 58, 1991, pp. 1–6.Google Scholar
  10. [10]
    A. Tate, A theory of the deceleration of long rods after impact, J. Mech. Phys. Solids 15, 1967, pp. 287–399.CrossRefGoogle Scholar
  11. [11]
    J. A. Zukas, High velocity impact dynamics, Wiley Inter science, New York, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • J. Buchar
  • J. Hřebíček

There are no affiliations available

Personalised recommendations