Journal of Marine Science and Technology

, Volume 23, Issue 1, pp 52–66 | Cite as

Peridynamics simulation of the fragmentation of ice cover by blast loads of an underwater explosion

  • Qing Wang
  • Yi Wang
  • Yingfei ZanEmail author
  • Wei Lu
  • Xiaolong Bai
  • Jun Guo
Original article


A bond-based peridynamic approach was applied to investigate the fragmentation of ice cover by blast loads of an underwater explosion. A modified elastic micromodulus was proposed in peridynamics, which can describe the long-range force varying with distance between two particles. The elastic-brittle constitutive model was implemented in numerical model considering different compressive and tensile strength of ice. A blast loading generated by underwater explosion was analyzed, in which the effects of fluid–solid coupling and liquid jets were taken into account. In addition, the failure criterion is defined based on fracture toughness. The simulation results show a good agreement with the experimental data. Furthermore, the parameters that influence the fracture radius of the ice cover were also discussed.


Peridynamics Underwater explosion Numerical stimulation Ice cover 



The support of the Marine Engineering Equipment Scientific Research Project of Ministry of Industry and Information Technology of PRC, the National Science and Technology Major Project of China (Grant No. 2016ZX05057020), and the National Natural Science Foundation of China (No. 51639004) are gratefully acknowledged.


  1. 1.
    Barash RM (1966) Ice-breaking by explosives. J Nav Ordn Lab 13(5):13–29Google Scholar
  2. 2.
    Meilor M (1972) Data for ice blasting. USA Cold Reg Res 46(8):34–50Google Scholar
  3. 3.
    Mellor M (1982) Breaking ice with explosives. J USA Cold Reg Res 57(9):65–89Google Scholar
  4. 4.
    Mansour A, Seireg A (1983) A computer-based simulation of ice-breaking by impact. J Energ Resour Technol 105(4):448–453CrossRefGoogle Scholar
  5. 5.
    Belytschko T, Moes N, Usui S et al (2001) Arbitrary discontinuities in finite elements. Int J Numer Methods Eng 50(4):993–1013CrossRefzbMATHGoogle Scholar
  6. 6.
    Wells GN, Sluys LJ (2000) Application of embedded discontinuities for softening solids. Eng Fract Mech 65(2–3):263–281CrossRefGoogle Scholar
  7. 7.
    Leski A (2007) Implementation of the virtual crack closure technique in engineering FE calculations. Finite Elem Anal Des 43(3):261–268CrossRefGoogle Scholar
  8. 8.
    Mohammadi S (2008) Extended finite element method: for fracture analysis of structures. XFEM Fract Anal Com 45(22):5675–5687Google Scholar
  9. 9.
    Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1):175–209MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Ha YD, Bobaru F (2011) Dynamic brittle fracture captured with peridynamics. Eng Fract Mech 78(6):1156–1168CrossRefGoogle Scholar
  11. 11.
    Askari E, Xu JF, Silling SA (2006) Peridynamic analysis of damage and failure in composites. In: Proceedings of the 44th AIAA aerospace sciences meeting and exhibition. No. 2006-88, Reno, NevadaGoogle Scholar
  12. 12.
    Kilic B, Madenci E (2009) Structure stability and failure analysis using peridynamic theory. Int J Non-Linear Mech 44(8):845–854CrossRefzbMATHGoogle Scholar
  13. 13.
    Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83(17):1526–1535CrossRefGoogle Scholar
  14. 14.
    Bobaru F, Ha YD (2011) Adaptive refinement and multiscale modeling in 2D peridynamics. Int J Multiscale Comput Eng 9(6):635–660CrossRefGoogle Scholar
  15. 15.
    Silling SA (2003) Dynamic fracture modeling with a meshfree peridynamic code. Comput Fluid Solid Mech 87(43):641–644Google Scholar
  16. 16.
    Silling SA, Zimmermann M (2003) Abeyaratne deformation of a peridynamic bar. J Elast 73(1–3):173–190CrossRefzbMATHGoogle Scholar
  17. 17.
    Kilic B (2008) Peridynamic theory for trogressive failure prediction in homogeneous and heterogeneous materials. Ph.D. thesis, The University of Arizona, TucsonGoogle Scholar
  18. 18.
    Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fract 162(1):229–244CrossRefzbMATHGoogle Scholar
  19. 19.
    Brbaru F, Yang M, Alves LF et al (2009) Convergence, adaptive refinement, and scaling in 1D peridynamics. Int J Numer Methods Eng 77(6):852–877CrossRefzbMATHGoogle Scholar
  20. 20.
    Madenci E, Oterkus E (2014) Peridynamic theory and its applications. Springer, New York, pp 125–150CrossRefzbMATHGoogle Scholar
  21. 21.
    Schulson EM (2001) Brittle failure of ice. Eng Fract Mech 68(17):1839–1887CrossRefGoogle Scholar
  22. 22.
    Schulson EM (1990) The brittle compressive fracture of ice. Acta Metallurgica Et Materialia 38(10):1963–1976CrossRefGoogle Scholar
  23. 23.
    Kuehn GA, Schulson EM, Jones DE et al (1993) The compressive strength of ice cubes of different sizes. J Offshore Mech Arct Eng 115(2):142–148CrossRefGoogle Scholar
  24. 24.
    Karr D, Das S (1983) Ice strength in brittle and ductile failure modes. J Struct Eng 109(3):2802–2811CrossRefGoogle Scholar
  25. 25.
    Kundu T (1973) Fundamentals of fracture mechanics. Fundam Fract Mech Butterworth 1973:425–438Google Scholar
  26. 26.
    Liu HW, Miller KJ (1979) Fracture toughness of fresh-water ice. J Glaciol 22(86):135–143CrossRefGoogle Scholar
  27. 27.
    Cole RH (1948) Underwater explosions. Princeton University Press, PrincetonCrossRefGoogle Scholar
  28. 28.
    Liang CC, Tai YS (2006) Shock responses of a surface ship subjected to noncontact underwater explosions. Ocean Eng 33(5–6):748–772CrossRefGoogle Scholar
  29. 29.
    Geers TL, Hunter KS (2003) An integrated wave-effects model for an underwater explosion bubble. J Acoust Soc Am 111(4):1584–1601CrossRefGoogle Scholar
  30. 30.
    Taylor GT (1941) The pressure and impulse of submarine explosion waves on plates[R]. Ministry of Home Security Report, FC235Google Scholar
  31. 31.
    Blake JR (1988) The Kelvin impulse: application to cavitation bubble dynamics. Anziam J 30(2):127–146MathSciNetzbMATHGoogle Scholar
  32. 32.
    Todd FrederickHenry (1961) Ship hull vibration. Princeton, E. ArnoldGoogle Scholar
  33. 33.
    Zhang ZH, Liang XQ, Xu W et al (2015) Numerical analysis of effect of different charge position on ice blasting. Blasting 32(4):118–127Google Scholar
  34. 34.
    Liu DC, Meng WY, Zhang DX et al (2011) Analysis of the dynamic response of the icecap structure under the action of explosion wave. J North China Inst Water Conserv Hydroelectr Power 39(17):95–98Google Scholar
  35. 35.
    Meng WY, Liu X, Hu JQ (2013) Numerical simulation and experiment research of ice blasting based on shaped charge technology. J North China Inst Water Conserv Hydroelectr Power 34(3):44–47Google Scholar

Copyright information

© JASNAOE 2017

Authors and Affiliations

  1. 1.College of Shipbuilding EngineeringHarbin Engineering UniversityHarbinChina

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