Peridynamics Modeling of a Shock Wave Perturbation Decay Experiment in Granular Materials with Intra-granular Fracture

Abstract

The shock wave perturbation decay experiment is a technique in which the evolution of a perturbation in a shock wave front is monitored as it propagates through a material field. This tool has recently been explored to probe the high-rate shear response of granular materials. This dynamic behavior is complicated due to inter- and intra-granular phenomena involved. Mesoscale modeling can give insight into this complexity by explicitly resolving the interactions and deformation of individual grains. The peridynamic theory, which is a nonlocal continuum theory, provides a suitable framework for modeling dynamic problems involving fracture. Prior research has focused mostly on the continuum, bulk response, neglecting any localized material failure, of granular materials. A systematic investigation of the effects of grain fracture and frictional contact forces between grains on the continuum behavior of granular materials is carried out by peridynamic simulations of a shock wave perturbation decay experiment. A sensitivity assessment of dominant factors indicates that grain fracture, a phenomenon ignored in most computational investigations of granular materials, plays a large role in the bulk dynamic response. Our results show that the wave propagates faster with an increase in the toughness of the material and the inter-particle friction. Also, the shock amplitude is shown to decay faster in tougher materials. It is further confirmed that under strong compression self-contact among fractured grain sub-particles cannot be neglected.

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References

  1. 1.

    Sakharov AD, Zaidel RM, Mineev VN, Oleinik AG (1965) Experimental investigation of the stability of shock waves and the mechanical properties of substances at high pressures and temperatures. Sov Phys JETP 9:1091–1094

    Google Scholar 

  2. 2.

    Mineev VN, Savinov EV (1967) Viscosity and melting point of aluminum, lead, and sodium chloride subjected to shock compression. Sov Phys JETP 25:411–416

    Google Scholar 

  3. 3.

    Mineev VN, Zaidel RM (1968) The viscosity of water and mercury under shock loading. Sov Phys JETP 27:874–878

    Google Scholar 

  4. 4.

    Miller GH, Ahrens TJ (1991) Shock-wave viscosity measurement. Rev Mod Phys 63(4):919–948

    Article  Google Scholar 

  5. 5.

    Mineev VN, Funtikov AI (2004) Viscosity measurements on metal melts at high pressure and viscosity calculations for the Earth’s core. Phys-Uspekhi 47:671–686

    Article  Google Scholar 

  6. 6.

    Mineev VN, Funtikov AI (2005) Measurements of the viscosity of water under shock compression. High Temp 43:141–150

    Article  Google Scholar 

  7. 7.

    Mineev VN, Funtikov AI (2006) Measurements of the viscosity of iron and uranium under shock compression. High Temp 44:941–949

    Article  Google Scholar 

  8. 8.

    Liu FS, Yang MX, Liu QW, Chen JX, Jing FQ (2005) Shear viscosity of aluminum under shock compression. Chin Phys Lett 22:747–749

    Article  Google Scholar 

  9. 9.

    Li-Peng F, Fu-Sheng L, Xiao-Juan M, Bei-Jing Z, Ning-Chao Z, Wen-Peng W, Bin-Bin H (2013) A fiber-array probe technique for measuring the viscosity of a substance under shock compression. Chin Phys B 22:108301

    Article  Google Scholar 

  10. 10.

    Li Y, Liu F, Ma X, Li Y, Yu M, Zhang J, Jing F (2009) A flyer-impact technique for measuring viscosity of metal under shock compression. Rev Sci Instrum 80(1):013903

    Article  Google Scholar 

  11. 11.

    Ma XJ, Liu FS, Zhang MJ, Sun YY (2011) Viscosity of aluminum under shock-loading conditions. Chin Phys B 20:068301

    Article  Google Scholar 

  12. 12.

    Li YL, Liu FS, Zhang MJ, Ma XJ, Li YL, Zhang JC (2009) Measurement on effective shear viscosity coefficient of iron under shock compression at 100 GPa. Chin Phys Lett 26:038301

    Article  Google Scholar 

  13. 13.

    Ma X, Liu FS, Sun Y, Zhang M, Peng X, Li Y (2011) Effective shear viscosity of iron under shock-loading condition. Chin Phys Lett 28:044704

    Article  Google Scholar 

  14. 14.

    Vogler TJ (2015) Shock wave perturbation decay in granular materials. J Dyn Behav Mat 1:370–387

    Article  Google Scholar 

  15. 15.

    Vogler TJ, Behzadinasab M, Rahman R, Foster JT (2016) Perturbation decay experiments on granular materials. Sandia National Laboratories Report 2016

  16. 16.

    Benson DJ (1997) The numerical simulation of the dynamic compaction of powders. In: Davison L, Horie Y, Shahinpoor M (eds) High-pressure shock compression of solids IV: response of highly porous solids to shock loading. Springer, New York, pp 233–255

    Google Scholar 

  17. 17.

    Borg JP, Vogler TJ (2008) Mesoscale calculations of the dynamic behavior of a granular ceramic. Int J Solids Struct 45:1676–1696

    Article  Google Scholar 

  18. 18.

    Borg JP, Vogler TJ (2009) Aspects of simulating the dynamic compaction of a granular ceramic. Modell Simul Mater Sci Eng 17:045003

    Article  Google Scholar 

  19. 19.

    Borg JP, Vogler TJ (2013) Rapid compaction of granular materials: characterizing two and three-dimensional mesoscale simulations. Shock Waves 23:153–176

    Article  Google Scholar 

  20. 20.

    Dwivedi SK, Teeter RD, Felice CW, Gupta YM (2008) Two dimensional mesoscale simulations of projectile instability during penetration in dry sand. J Appl Phys 104:083502

    Article  Google Scholar 

  21. 21.

    Dwivedi SK, Pei L, Teeter RD (2015) Two-dimensional mesoscale simulations of shock response of dry sand. J Appl Phys 117:085902

    Article  Google Scholar 

  22. 22.

    Lammi CJ, Vogler TJ (2012) Mesoscale simulations of granular materials with peridynamics. In: Elert ML (ed) Shock compression of condensed matter-2011. American Institute of Physics, New York, pp 1467–1470

    Google Scholar 

  23. 23.

    Vogler TJ, Borg JP, Grady DE (2012) On the scaling of steady structured waves in heterogeneous materials. J Appl Phys 112:123507

    Article  Google Scholar 

  24. 24.

    Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48:175–209

    Article  Google Scholar 

  25. 25.

    Silling SA (2003) Dynamic fracture modeling with a meshfree peridynamic code. In: Bathe KJ (ed) Computational fluid and solid mechanics. Elsevier, Amsterdam, p 641644

    Google Scholar 

  26. 26.

    Foster JT, Silling SA, Chen WW (2010) Viscoplasticity using peridynamics. Int J Numer Meth Eng 81:1242–1258

    Google Scholar 

  27. 27.

    Silling SA, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamic states and constitutive modeling. J Elast 88:151–84

    Article  Google Scholar 

  28. 28.

    Silling SA, Askari E (2005) A meshfree method based on the peridynamic model of solid mechanics. Comput Struct 83:1526–1535

    Article  Google Scholar 

  29. 29.

    Silling SA, Askari E (2004) Peridynamic modeling of impact damage. In: ASME/JSME 2004 pressure vessels and piping conference. American Society of Mechanical Engineers, pp 197-205

  30. 30.

    Behzadinasab M, Vogler TJ, Foster JT (2018) Modeling perturbed shock wave decay in granular materials with intra-granular fracture. In: AIP conference proceedings of the 20th APS-SCCM, vol 1979

  31. 31.

    Parks ML, Littlewood DJ, Mitchell JA, Silling SA (2012) Peridigm users guide. Sandia National Laboratories Report 2012

  32. 32.

    Heroux MA, Bartlett RA, Howle VE, Hoekstra RJ, Hu JJ, Kolda TG, Salinger AG (2005) An overview of the Trilinos project. ACM TOMS 31:397–423

    Article  Google Scholar 

Download references

Acknowledgements

We greatly appreciate the financial support from the AFOSR MURI Center for Materials Failure Prediction through Peridynamics and Sandia National Laboratories. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

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Correspondence to M. Behzadinasab.

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Behzadinasab, M., Vogler, T.J., Peterson, A.M. et al. Peridynamics Modeling of a Shock Wave Perturbation Decay Experiment in Granular Materials with Intra-granular Fracture. J. dynamic behavior mater. 4, 529–542 (2018). https://doi.org/10.1007/s40870-018-0174-2

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Keywords

  • Shock loading
  • Perturbation decay experiment
  • Granular materials
  • Mesoscale modeling
  • Peridynamics
  • Fracture
  • Contact
  • Friction