Skip to main content
Log in

Simulation of explosively driven metallic tubes by the cylindrical smoothed particle hydrodynamics method

  • Original Article
  • Published:
Shock Waves Aims and scope Submit manuscript

Abstract

Modified cylindrical smoothed particle hydrodynamics (MCSPH) approximation equations are derived for hydrodynamics with material strength in axisymmetric cylindrical coordinates. The momentum equation and internal energy equation are represented to be in the axisymmetric form. The MCSPH approximation equations are applied to simulate the process of explosively driven metallic tubes, which includes strong shock waves, large deformations and large inhomogeneities, etc. The meshless and Lagrangian character of the MCSPH method offers the advantages in treating the difficulties embodied in these physical phenomena. Two test cases, the cylinder test and the metallic tube driven by two head-on colliding detonation waves, are presented. Numerical simulation results show that the new form of the MCSPH method can predict the detonation process of high explosives and the expansion process of metallic tubes accurately and robustly.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15

Similar content being viewed by others

References

  1. Kury, J.W., Hornig, H.C., Lee, E.L., McDonnel, J.L., Ornellas, D.L., Finger, M., Strange, F.M., Wilkins, M.L.: Metal acceleration by chemical explosives. In: 4th Symposium on Detonation. ACR-126, Office of Naval Research (1965)

  2. Gurney, R.W.: The initial velocities of fragments from bombs, shells and grenades. BRL Report No. 405 (1943)

  3. Taylor, G.I.: The fragmentation of tubular bombs. Sci. Pap. GI Taylor 3(41), 387–390 (1963)

    Google Scholar 

  4. Martineau, R.L., Anderson, C.A., Smith, F.W.: Expansion of cylindrical shells subjected to internal explosive detonations. Exp. Mech. 40(2), 219–225 (2000)

    Article  Google Scholar 

  5. Martineau, R.L., Prime, M.B., Anderson, C.A., Smith, F.W.: An Explicit Model of Expanding Cylindrical Shells Subjected to High Explosive Detonations. Los Alamos National Lab, Los Alamos (1999)

    Book  Google Scholar 

  6. Martineau, R.L., Anderson, C.A.: A Viscoplastic Model of Expanding Cylindrical Shells Subjected to High Explosive Detonations. Los Alamos National Lab, Los Alamos (1998)

    Google Scholar 

  7. Anderson, C.E., Predebon, W.W., Karpp, R.R.: Computational modeling of explosive-filled cylinders. Int. J. Eng. Sci. 23, 1317–1330 (1985)

    Article  Google Scholar 

  8. Tang, P.K.: Modeling hydrodynamic behaviors in detonation. Propellants Explos. Pyrotech. 16(5), 240–244 (1991)

    Article  Google Scholar 

  9. Zhang, S.W., Hua, J.S., Liu, C.L., Han, C.S., Wang, D.S., Sun, X.L., Zhang, Z.T.: A numerical simulation of the metallic tube expansion induced by inside head-on hitting two detonation waves. Explos. Shock Waves 24(3), 219–225 (2004). (in Chinese)

    Google Scholar 

  10. Zhang, C.Y., Gu, Y., Zhang, S.W., Sun, X.L., Peng, Q.X.: Study on expanding characteristic of steel tube driven by two head-on colliding detonation waves. Explos. Shock Waves 25(3), 222–226 (2005). (in Chinese)

    Google Scholar 

  11. Gingold, R.A., Monaghan, J.J.: Smoothed particle hydrodynamics: theory and application to non-spherical stars. Mon. Not. R. Astron. Soc. 181, 375–389 (1977)

    Article  MATH  Google Scholar 

  12. Lucy, L.B.: A numerical approach to the testing the fission hypothesis. Astron. J. 82, 1013–1024 (1977)

    Article  Google Scholar 

  13. Liberskty, L.D., Petschek, A.G., Carney, T.C., Hipp, J.R., Allahdadi, F.A.: High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response. J. Comput. Phys. 109(1), 67–75 (1993)

    Article  Google Scholar 

  14. Liu, M.B., Liu, G.R., Zong, Z.: An overview on smoothed particle hydrodynamics. Int. J. Comput. Methods 5(1), 135–188 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  15. Liu, M.B., Liu, G.R., Lam, K.Y.: Adaptive smoothed particle hydrodynamics for high strain hydrodynamics with material strength. Shock Waves 15(1), 21–29 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  16. Swegle, J.W., Attaway, S.W.: On the feasibility of using smoothed particle hydrodynamics for underwater explosion calculations. Comput. Mech. 17(3), 151–168 (1995)

    Article  MATH  Google Scholar 

  17. Liu, M.B., Liu, G.R., Lam, K.Y.: Investigations into water mitigation using a meshless particle method. Shock Waves 12(3), 181–195 (2002)

    Article  Google Scholar 

  18. Liu, M.B., Liu, G.R., Lam, K.Y., Zong, Z.: Meshfree particle simulation of the detonation process for high explosives in shaped charge unlined cavity configurations. Shock Waves 12(6), 509–520 (2003)

    Article  Google Scholar 

  19. Brookshaw, L.: Smooth particle hydrodynamics in cylindrical coordinates. ANZIAM J. 44, 114–139 (2003)

    MathSciNet  Google Scholar 

  20. Omang, M., Trulsen, J., Børve, S.: SPH in spherical and cylindrical coordinates. J. Comput. Phys. 213(1), 391–412 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  21. García-Senz, D., Relano, A., Cabezón, R.M., Bravo, E.: Axisymmetric smoothed particle hydrodynamics with self-gravity. Mon. Not. R. Astron. Soc. 392, 346–360 (2009)

    Article  Google Scholar 

  22. Petschek, A.G., Libersky, L.D.: Cylindrical smoothed particle hydrodynamics. J. Comput. Phys. 109(1), 76–83 (1993)

    Article  MATH  Google Scholar 

  23. Seo, S., Min, O.: Axisymmetric SPH simulation of elasto-plastic contact in the low velocity impact. Comput. phys. Commun. 175(9), 583–603 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  24. Batra, R.C., Zhang, G.M.: Modified smoothed particle hydrodynamics (MSPH) basis functions for meshless methods, and their application to axisymmetric Taylor impact test. J. Comput. Phys. 227(3), 1962–1981 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  25. Liu, G.R., Liu, M.B.: Smoothed Particle Hydrodynamics: A Meshfree Particle Method. World Scientific, Singapore (2003)

    Book  Google Scholar 

  26. Monaghan, J.J.: Smoothed particle hydrodynamics. Rep. Prog. Phys. 68(8), 1703–1759 (2005)

    Article  MathSciNet  Google Scholar 

  27. Monaghan, J.J.: Smoothed particle hydrodynamics. Annu. Rev. Astron. Astrophys. 30, 543–574 (1992)

    Article  Google Scholar 

  28. Benz, W.: Applications of smooth particle hydrodynamics (SPH) to astrophysical problems. Comput. Phys. Commun. 48(1), 97–105 (1988)

    Article  Google Scholar 

  29. Johnson, G.R., Cook, W.H.: A constitutive model and data for metals subjected to large strains, high strain rates and high temperatures. In: Proceedings of the 7th International Symposium on Ballistics, 21, 541-547 (1983)

  30. Steinberg, D.J., Cochran, S.G., Guinan, M.W.: A constitutive model for metals applicable at high-strain rate. J. Appl. Phys. 51(3), 1498–1504 (1980)

    Article  Google Scholar 

  31. Dobratz, B.M., Crawford, P.C.: LLNL Explosives Handbook. UCRL-52997 Rev. 2 (1985)

  32. LS-DYNA Keyword User’s Manual, Volume 1, Version R7.0, Livermore Software Technology Corporation (LSTC). Livermore (2013)

  33. Chen, J., Sun, C.W., Pu, Z.M., Zhang, G.S., Gao, N.: Expansion of metallic tubes driven by detonation product behind two head-on colliding detonation waves. Explos. Shock Wave 23(5), 442–447 (2003). (in Chinese)

    Google Scholar 

  34. Zukas, J.A.: High Velocity Impact Dynamics. Wiley, New York (1990)

    Google Scholar 

  35. Johnson, G.R., Cook, W.H.: Fracture characteristics of three metals subjected to various strains, strain rates, temperatures, and pressures. Eng Fract. Mech. 21(1), 31–48 (1985)

    Article  Google Scholar 

  36. Chen, G., Chen, Z.F., Tao, J.L., Niu, W., Zhang, Q.P., Huang, X.C.: Investigation and validation on plastic constitutive parameters of 45 steel. Explos. Shock Waves 25(5), 451–456 (2005). (in Chinese)

    Google Scholar 

Download references

Acknowledgments

The financial support from the National Natural Science Foundation of China (11272118) is gratefully acknowledged.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. Yang.

Additional information

Communicated by N. Thadhani and A. Higgins.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yang, G., Han, X. & Hu, D.A. Simulation of explosively driven metallic tubes by the cylindrical smoothed particle hydrodynamics method. Shock Waves 25, 573–587 (2015). https://doi.org/10.1007/s00193-015-0588-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00193-015-0588-x

Keywords

Navigation