A generalized formula for the penetration depth of a deformable projectile

M. B. Rubin, A. L. Yarin

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


A simple analytical algebraic formula is developed for predicting the penetration depth of a deformable projectile into a semi-infinite target. This formula is a simplified version of more general equations that have been developed to predict the time-dependent penetration process in finite thickness targets. Specifically, the formula generalizes the classical hydrodynamic theory to include dependence on elastic properties of the target and on the yield strengths of both the target and the projectile. Moreover, the formula is limited to the case of long-rod penetration where both the projectile and the target experience significant plastic flow. The limiting values of the location of the elastic-plastic boundary in the target have been determined, and a single empirical constant has been introduced to characterize the transition between these limiting values. A value for this empirical constant has been determined which produces theoretical predictions that are in reasonable agreement with experimental data for moderate to high values of the impact velocity of steel and tungsten projectiles penetrating a steel target.

Original languageEnglish
Pages (from-to)387-398
Number of pages12
JournalInternational Journal of Impact Engineering
Issue number4
Publication statusPublished - 2002 Apr

Bibliographical note

Funding Information:
This work was partially supported by the Fund for Promotion of Research at Technion. Also, the authors would like to acknowledge helpful comments from an anonymous reviewer.


  • Algebraic formula
  • Deformable projectile
  • Penetration depth

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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