Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Characterization of hole-diameter in thin metallic plates perforated by spherical projectiles using genetic algorithms

  • 126 Accesses

  • 4 Citations


The empirical and semi-empirical models available in literature for the estimation of hole-diameter in thin metallic plates by the strike of spherical projectile are mostly valid for the data for which these have been developed. This may be partly attributed to the form of the model employed for their development. The behavioural constraints and the limiting conditions are not satisfied by these models. In the present paper, some of the non-dimensional models have been developed that satisfy the behavioural constraints and limiting conditions. The data used in the development of earlier statistical models has been reanalyzed for the development of new models for the characterization of hole-diameter with a view towards seeing whether better characterization is possible. The genetic algorithm coupled with the penalty function method has been used for the constrained optimization of model parameters that result in low errors and high correlation coefficients.

This is a preview of subscription content, log in to check access.


c p , c t :

Speed of sound in projectile and target materials, respectively

ρ p , ρ t :

Density of projectile and target materials, respectively

D p :

Diameter of spherical projectile

D h :

Hole-diameter in target plate

T t :

Target thickness

V :

Velocity of strike of projectile

σ US :

Shear strength of the target material

θ :

Angle of strike or spray angle of projectile


  1. 1

    Klinkrad H.: Space Debris—Models and Risk Analysis. Springer, Berlin (2006)

  2. 2

    Chhabildas, L.C., Hertel, E.S., Jr. Reinhart, W.D., Miller, R.M.: Whipple Bumper Shield and CTH Simulations at Velocities in Excess of 10 km/s. SANDIA report SAND91-2683 (1992)

  3. 3

    Whipple F.L.: Meteorites and space travel. Astron. J. 52(116), 131 (1947)

  4. 4

    De Chant, L.J.: A High Velocity Plate Penetration Hole Diameter Relationship Based on Late Time Stagnation Point Flow Concepts. Unpublished manuscript, Available from ljdecha@sandia.gov (2004a)

  5. 5

    De Chant, L.J.: Validation of a computational implementation of the Grady–Kipp dynamic fragmentation theory for thin metal plate impacts using an analytical strain-rate model and hydrodynamic analogues. Mech. Mater. (2004b, in press)

  6. 6

    De Chant L.J.: A explanation for the minimal effect of body curvature on hypervelocity penetration hole formation. Int. J. Solids Struct. 41, 4163–4177 (2004)

  7. 7

    Hill S.A.: Determination of an empirical model for the prediction of penetration hole diameter in thin plates from hypervelocity impact. Int. J. Impact Eng. 30, 303–321 (2004)

  8. 8

    Garadner D.J., McDonnel J.M., Collier I.: Hole growth characterisation for hypervelocity impacts in thin targets. Int. J. Impact Eng. 19(7), 589–602 (1997)

  9. 9

    Schonberg W.P.: Hypervelocity impact penetration phenomena in Aluminum space structures. J. Aerosp. Eng. 3(3), 173–185 (1990)

  10. 10

    Hosseini M., Abbas H.: Neural network approach for estimation of hole-diameter in thin plates perforated by spherical projectiles. Thin-Walled Struct. 46(6), 592–601 (2008)

  11. 11

    Forrest S.: Genetic algorithms. ACM Comput. Surv. 28(1), 77–80 (1996)

  12. 12

    Maiden C.J., Gehring J.W., McMillan A.R.: Investigation of fundamental mechanism of damage to thin targets by hypervelocity projectiles. In: General Motors Corporation Final Report No. TR63-225 GM Defense Research Laboratory, Santa Barbara (1963)

  13. 13

    McMillan A.R.: Experimental Investigations of Simulated Meteoroid Damage to Various Spacecraft Structures. NASA CR-915, Washington (1968)

  14. 14

    Herrmann, W., Jones, A.H.: Survey of Hypervelocity Impact Information. Massachusetts Institute of Technology, ASRL Report No. 99-1 (1961)

  15. 15

    Tipton, J.: HULL Hydrocode Analysis Results Presented at NASA/MSFC WP01 Meteoroid/Orbital Debris Working Group, NASA Purchase Order, USACOE, Huntsville, Alabama (1991–1993)

  16. 16

    Piekutowski A.J.: Formation and Description of Debris Clouds Produced by Hypervelocity Impact. NASA CR-4707, Washington (1996)

  17. 17

    Piekutowski A.J.: Holes produced in thin aluminum sheets by the hypervelocity impact of aluminum spheres. Int. J. Impact Eng. 23, 711–722 (1999)

  18. 18

    Edwards M.R., Mathewson A.: The ballistic properties of tool steel as a potential improvised armour plate. Int. J. Impact Eng. 19(4), 297–309 (1997)

  19. 19

    Atkins A.G., Khan M.A., Liu J.H.: Necking and radial cracking around perforations in thin sheets at normal incidence. Int. J. Impact Eng. 21(7), 521–539 (1998)

  20. 20

    Wierzbicki T.: Petalling of plates under explosive and impact loading. Int. J. Impact Eng. 22, 935–954 (1999)

  21. 21

    Shen W.Q., Rieve R.O., Baharun B.: A study on the failure of circular plates struck by masses. Part 1: experimental results. Int. J. Impact Eng. 27, 399–412 (2002)

  22. 22

    Lee Y.W., Wierzbicki T.: Fracture prediction of thin plates under localized impulsive loading. Part II: discing and petalling. Int. J. Impact Eng. 31, 1277–1308 (2005)

  23. 23

    Piekutowski A.J.: Debris clouds generated by hypervelocity impact of cylindrical projectiles with thin aluminium plates. Int. J. Impact Eng. 5(1–4), 509–518 (1987)

  24. 24

    Teng X., Wierzbicki T., Hiermaier S., Rohr I.: Numerical prediction of fracture in the Taylor test. Int. J. Solids Struct. 42, 2929–2948 (2005)

  25. 25

    Fleming P., Purshouse R.C.: Evolutionary algorithms in control systems engineering: a survey. Control Eng. Practice 10, 1223–1241 (2002)

  26. 26

    Mitchell M.: An Introduction to Genetic Algorithms. MIT Press, Cambridge (1996)

  27. 27

    Schulze-Kremer S.: Molecular Bioinformatics—Algorithms and Applications. de Gruyter, New York (1995)

  28. 28

    Kitano, H.: Empirical studies on the speed of convergence of neural network training using genetic algorithms. In: AAAI-90 Proceedings

  29. 29

    Michalewicz Z.: Genetic Algorithms + Data Structures = Evolution Programs. 2nd edn. Springer, New York (1994)

  30. 30

    Maiden C.J., Gehring J.W., McMillan A.R.: Investigation of Fundamental Mechanism of Damage to Thin Targets by Hypervelocity Projectiles. NASA TR63-225, GM Defense Research Laboratory, Washington (1963)

  31. 31

    Sawle, D.R.: Hypervelocity Impact in Thin Sheets, Semi-Infinite Targets at 15 km/s. AIAA Paper No. 69-378, AIAA Hypervelocity Impact Conference, Cincinnati (1969)

  32. 32

    Sorenson, N.R.: Systematic investigation of crater formations in metals. In: Proceedings of the 7th Hypervelocity Impact Symposium, vol. 6, pp. 281–325 (1964)

  33. 33

    Nysmith C.R., Denardo B.P.: Experimental Investigation of the Momentum Transfer Associated with Impact into Thin Aluminum Targets. NASA TND-5492, Washington (1969)

  34. 34

    Hosseini M., Abbas H.: Growth of hole in thin plates under hypervelocity impact of spherical projectiles. J. Thin-Walled Struct. 44(9), 1006–1016 (2006)

  35. 35

    Rolsten R.F., Wellnitz J.N., Hunt H.H.: An example of hole diameter in thin plates due to hypervelocity impact. J. APPl. Phys. 34(3), 556–559 (1964)

  36. 36

    Carey, W.C., McDonnell, J.A.M., Dixon, DG.: Capture cells: decoding the impacting projectile parameters. In: Lunar and Planetary Science Conference XVIth, Abstracts (1985)

Download references

Author information

Correspondence to H. Abbas.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Abbas, H., Alsayed, S.H., Almusallam, T.H. et al. Characterization of hole-diameter in thin metallic plates perforated by spherical projectiles using genetic algorithms. Arch Appl Mech 81, 907–924 (2011). https://doi.org/10.1007/s00419-010-0459-y

Download citation


  • Genetic algorithm
  • Hole-diameter
  • Projectile
  • Hypervelocity impact
  • Spherical projectile