Penetration of a rigid projectile into an elastic-plastic target of finite thickness

A. L. Yarin, M. B. Rubin, I. V. Roisman

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77 Citations (Scopus)


This paper considers the problem of non-steady penetration of a rigid projectile into an elastic-plastic target of finite thickness. A specific blunt projectile shape in the form of an ovoid of Rankine is used because it corresponds to a reasonably simple velocity field which exactly satisfies the continuity equation and the condition of impenetrability of the projectile. The target region is subdivided into an elastic region ahead of the projectile where the strains are assumed to be small, and a rigid-plastic region near the projectile where the strains can be arbitrarily large. Using the above mentioned velocity field, the momentum equation is solved exactly in both the elastic and the rigid-plastic regions to find expressions for the pressure and stress fields. The effects of the free front and rear surfaces of the target (which is presumed not to be too thin) and the separation of the target material from the projectile are modeled approximately, and the force applied to the projectile is calculated analytically. An equation for projectile motion is obtained which is solved numerically. Also, a useful simple analytical solution for the depth of penetration or the residual velocity is developed by making additional engineering approximations. Moreover, the solution procedure presented in this paper permits a straight forward approximate generalization to accommodate a projectile with arbitrary shaped tip. Theoretical predictions are compared with numerous experimental data on normal penetration in metal targets, and the agreement of the theory with experiments is good even though no empirical parameters are used. Also, simulations for conical and hemispherical tip shapes indicate that the exact shape of the projectile tip does not significantly influence the prediction of integral quantities like penetration depth and residual velocity.

Original languageEnglish
Pages (from-to)801-831
Number of pages31
JournalInternational Journal of Impact Engineering
Issue number5-6
Publication statusPublished - 1995

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Automotive Engineering
  • Aerospace Engineering
  • Safety, Risk, Reliability and Quality
  • Ocean Engineering
  • Mechanics of Materials
  • Mechanical Engineering


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