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Analytical and Energy-Based Methods for Penetration Mechanics


Analytical methods; Energy-based methods; Impact; Penetration and perforation mechanics; Petalling; Plugging


The terms perforation and penetration are used frequently throughout this chapter. It should however be noted that there is a significant difference between the two terms. Penetration refers to the ballistic impact of a target which results in the projectile becoming embedded or ricocheting off the target. Perforation describes the projectile impacting the target and passing completely through it. Plugging refers to the mechanical process of the formation of a plug of target material once it has been impacted by a projectile.


A comprehensive understanding of ballistic impact has been essential ever since the invention of rudimentary weapons such as the bow and arrow. There has been since then a need to develop effective means of protection such as the shield. The rapid advancement of weapon technology has led to the progress of protective...


  • Ballistic Limit Velocity (BLV)
  • Petala
  • Ductile Hole Growth
  • Residual Velocity
  • Free Impact

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  • Atkins AG, Afzal Khan M, Liu JH (1998) Necking and radial cracking around perforations in thin sheets at normal incidence. Int J Impact Eng 21:521–539

    CrossRef  Google Scholar 

  • Awerbuch J, Bodner SR (1973) Experimental investigation of normal perforation of projectiles in metallic plates. Technical report, National Technical Information service, Springfield

    Google Scholar 

  • Borvik T (2000) Ballistic penetration and perforation of steel plates. Technical report, Norwegian University of Science and Technology – NUST

    Google Scholar 

  • Borvik T, Leinum JR, Solberg JK, Hopperstad OS, Langseth M (2001) Observations on shear plug formation in Weldox 460e steel plates impacted by blunt-nosed projectiles. Int J Impact Eng 25:553–572

    CrossRef  Google Scholar 

  • Cao S, Zhang W, Deng T, Wei G (2012) Experimental investigation on the ballistic performance of monolithic and layered metal plates subjected to impact by blunt rigid projectiles. Int J Impact Eng 49:115–129

    CrossRef  Google Scholar 

  • Goldsmith W (2001) Impact: the theory and physical behaviour of colliding solids. Dover Publications Inc., New York

    MATH  Google Scholar 

  • Greszczuk LB, Zukas JA, Nicholas T, Swift HF, Curran DR (1982) Impact dynamics. Wiley, New York

    Google Scholar 

  • Horne MR (1979) Plastic theory of structures, Pergamon Press, Oxford

    Google Scholar 

  • Jaramaz S, Elek P, Mickovic D (2005) Modeling of perforation of plates and multilayered metal targets. Int J Solids Struct 42:1209–1224

    CrossRef  Google Scholar 

  • Jia X, Huang Z, Zu X, Gu X, Xiao Q (2014) Theoretical analysis of the disturbance of shaped charge jet penetrating a woven fabric rubber composite armor. Int J Impact Eng 65:69–78

    CrossRef  Google Scholar 

  • Krauthammer T (2008) Modern protective structures. CRC Press, Boca Raton

    CrossRef  Google Scholar 

  • Landkof B, Goldsmith W (1985) Petalling of thin, metallic plates during penetration by cylindro-conical projectiles. Int J Solids Struct 21:245–266

    CrossRef  Google Scholar 

  • Mackman ME, Goldsmith W (1978) The mechanics of penetration of projectiles into targets. Int J Sci 16:1–99

    Google Scholar 

  • Recht RF, Ipson TW (1963) Ballistic perforation dynamics. J Appl Mech 30:384–390

    CrossRef  Google Scholar 

  • Taylor G (1948) The formation and enlargement of a circular hole in a thin plastic sheet. Q J Mech Appl Math 1:103–124

    MathSciNet  CrossRef  Google Scholar 

  • Thomson WT (1955) An approximate theory of armor penetration. J Appl Phys 26:80–82

    CrossRef  Google Scholar 

  • Velmurugan R, Sikarwar RS, Gupta NK (2014) Influence of fibre orientation and thickness on the response of glass/epoxy composites subjected to impact loading. Compos Part B 60:627–636

    CrossRef  Google Scholar 

  • Woodward RL, de Morton ME (1987) A structural model for thin plate perforation by normal impact of blunt projectiles. Int J Impact Eng 6:129–140

    CrossRef  Google Scholar 

  • Zhang TG, Stronge WJ (1996) Theory for ballistic limit of thin ductile tubes hit by blunt missiles. Int J Impact Eng 18:735–752

    CrossRef  Google Scholar 

  • Zukas JA (1980) Impact dynamics: theory and experiments. Technical report, US Army Armament Research and Development Command, Maryland

    Google Scholar 

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Correspondence to F. Teixeira-Dias .

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Teixeira-Dias, F., Smith, N., Galiounas, E. (2018). Analytical and Energy-Based Methods for Penetration Mechanics. In: Altenbach, H., Öchsner, A. (eds) Encyclopedia of Continuum Mechanics. Springer, Berlin, Heidelberg.

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