Acta Mechanica Sinica

, Volume 35, Issue 4, pp 852–865 | Cite as

Analysis of the velocity relationship and deceleration of long-rod penetration

  • W. J. Jiao
  • X. W. ChenEmail author
Research Paper


The relationship between the average penetration velocity, \( \bar{U} \), and the initial impact velocity, \( V_{ 0} \), in long-rod penetration has been studied recently. Experimental and simulation results all show a linear relationship between \( \bar{U} \) and \( V_{ 0} \) over a wide range of \( V_{ 0} \) for different combinations of rod and target materials. However, the physical essence has not been fully revealed. In this paper, the \( \bar{U} - V_{ 0} \) relationship is comprehensively analyzed using the hydrodynamic model and the Alekseevskii–Tate model. In particular, the explicit \( \bar{U} - V_{ 0} \) relationships are derived from approximate solutions of the Alekseevskii–Tate model. In addition, the deceleration in long-rod penetration is discussed. The deceleration degree is quantified by a deceleration index, \( \alpha = {{2\bar{\mu }} \mathord{\left/ {\vphantom {{2\bar{\mu }} {(K\varPhi_{Jp} )}}} \right. \kern-0pt} {(K\varPhi_{Jp} )}} \approx Y_{p} \rho_{p}^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-0pt} 2}}} \left( {\rho_{p}^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-0pt} 2}}} + \rho_{t}^{{{{ - 1} \mathord{\left/ {\vphantom {{ - 1} 2}} \right. \kern-0pt} 2}}} } \right)V_{0}^{ - 2} , \) which is mainly related to the impact velocity, rod strength, and rod/target densities. Thus, the state of the penetration process can be identified and designed in experiments.


Long-rod penetration Average penetration velocity Initial impact velocity Alekseevskii–Tate model Deceleration 



The work was supported by the National Natural Science Foundation of China (Grant 11872118). The authors want to express deep gratitude to the reviewers for their sound comments and helpful suggestions.


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Modern MechanicsUniversity of Science and Technology of ChinaHefeiChina
  2. 2.Institute of Systems EngineeringChina Academy of Engineering PhysicsMianyangChina
  3. 3.The State Key Lab of Explosion Science and TechnologyBeijing Institute of TechnologyBeijingChina
  4. 4.Advanced Research Institute of Multidisciplinary ScienceBeijing Institute of TechnologyBeijingChina

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