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Computational Mechanics

, Volume 55, Issue 2, pp 287–302 | Cite as

A peridynamics–SPH coupling approach to simulate soil fragmentation induced by shock waves

  • Bo Ren
  • Houfu Fan
  • Guy L. Bergel
  • Richard A. Regueiro
  • Xin Lai
  • Shaofan LiEmail author
Original Paper

Abstract

In this work, a nonlocal peridynamics–smoothed particle hydrodynamics (SPH) coupling formulation has been developed and implemented to simulate soil fragmentation induced by buried explosions. A peridynamics–SPH coupling strategy has been developed to model the soil–explosive gas interaction by assigning the soil as peridynamic particles and the explosive gas as SPH particles. Artificial viscosity and ghost particle enrichment techniques are utilized in the simulation to improve computational accuracy. A Monaghan type of artificial viscosity function is incorporated into both the peridynamics and SPH formulations in order to eliminate numerical instabilities caused by the shock wave propagation. Moreover, a virtual or ghost particle method is introduced to improve the accuracy of peridynamics approximation at the boundary. Three numerical simulations have been carried out based on the proposed peridynamics–SPH theory: (1) a 2D explosive gas expansion using SPH, (2) a 2D peridynamics–SPH coupling example, and (3) an example of soil fragmentation in a 3D soil block due to shock wave expansion. The simulation results reveal that the peridynamics–SPH coupling method can successfully simulate soil fragmentation generated by the shock wave due to buried explosion.

Keywords

Explosion Fragmentation Peridynamics Shock wave SPH Soil mechanics 

Notes

Acknowledgments

This work was supported by an ONR MURI Grant N00014-11-1-0691. This support is gratefully acknowledged. In addition, Mr. Houfu Fan would like to thank the Chinese Scholarship Council (CSC) for a graduate fellowship.

References

  1. 1.
    Madenci E, Oterkus E (2014) Peridynamic theory and its applications. Springer, New YorkCrossRefzbMATHGoogle Scholar
  2. 2.
    Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48:175–209CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Bobaru F, Hu W (2012) The meaning, selection, and use of the peridynamics horizon and its relation to crack branching in brittle materials. Int J Fract 176:215–222CrossRefGoogle Scholar
  4. 4.
    Gerstle W, Sau N, Silling S (2007) Peridynamics modeling of concrete structures. Nucl Eng Des 237:1250–1258CrossRefGoogle Scholar
  5. 5.
    Askari A, Xu J, Silling S (2006) Peridynamics analysis of damage and failure in composites. In: 44th AIAA aerospace sciences meeting and exhibit. Reno, Nevada, AIAA-2006-88Google Scholar
  6. 6.
    Kilic B, Madenci E, Ambur DR (2006) Analysis of brazed single-lap joints using the peridynamics theory. In: 47th AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference. Newport, Rhode Island, AIAA-2006-2267Google Scholar
  7. 7.
    Silling SA, Askari E (2004) Peridynamics modeling of impact damage. In: Moody FJ (ed) Problems involving thermal-hydraulics, liquid sloshing, and extreme loads on structures, vol 489, PVPAmerican Society of Mechanical Engineers, New York, pp 197–205Google Scholar
  8. 8.
    Silling SA, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamics states and constitutive modeling. J Elast 88:151–184CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Silling SA, Lehoucq RB (2008) Convergence of peridynamics to classical elasticity theory. J Elast 93:13–37CrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Tupek MR, Rimoli JJ, Radovitzky R (2013) An approach for incorporating classical continuum damage models in state-based peridynamics. Comput Methods Appl Mech Eng 263:20C26CrossRefMathSciNetGoogle Scholar
  11. 11.
    Warren TL, Silling SA, Askari E, Weckner O, Epton MA, Xu J (2009) A non-ordinary state-based peridynamics method to model solid material deformation and fracture. Int J Solids Struct 46(5):1186–1195CrossRefzbMATHGoogle Scholar
  12. 12.
    Foster JT, Silling SA, Chen WW (2010) Viscoplasticity using peridynamics. Int J Numer Methods Eng 81:1242–1258zbMATHGoogle Scholar
  13. 13.
    Wecknera O, Mohamed NAN (2009) Viscoelastic material models in peridynamics. Appl Math Computat 219(11):6039–6043CrossRefGoogle Scholar
  14. 14.
    Tuniki BK (2012) Peridynamics constitutive model for concrete. Master thesis, Dept. of Civil Engineering, University of New Mexico, NM USAGoogle Scholar
  15. 15.
    Vermeer PA, Borst R (1984) Non-associated plasticity for soils, concrete, and rock. Heron 29(3):3–64Google Scholar
  16. 16.
    Matsuoka H, Nakai T (1974) Stress-deformation and strength characteristics of soil under three different principal stresses. Proc Jpn Soc Civil Eng 232:59–70CrossRefGoogle Scholar
  17. 17.
    Drucker DC, Prager W (1952) Soil mechanics and plastic analysis or limit design. Quart Appl Math 10(2):157–165zbMATHMathSciNetGoogle Scholar
  18. 18.
    Lammi CJ, Vogler TJ (2012) Mesoscale simulations of granular materials with peridynamics. Shock compressison of condensed matter-2011. Proceedings of the conference of the American Physical Society Topical Group on shock compression of condensed matter, vol 1426, pp 1467–1470Google Scholar
  19. 19.
    Lammi CJ, Zhou M (2013) Peridynamics simulation of inelasticity and fracture in pressure-dependent materials. The workshop on nonlocal damage and failure: peridynamics and other nonlocal models. San Antonio, TXGoogle Scholar
  20. 20.
    Alia A, Souli M (2006) High explosive simulation using multi-material formulations. Appl Therm Eng 26:1032C1042CrossRefGoogle Scholar
  21. 21.
    Gingold RA, Monaghan JJ (1977) Smoothed particle hydrodynamics—theory and application to non-spherical stars. Mon Not R Astron Soc 181:375–389CrossRefzbMATHGoogle Scholar
  22. 22.
    Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, SingaporeCrossRefGoogle Scholar
  23. 23.
    Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, Chichester, UKGoogle Scholar
  24. 24.
    Ren B, Li SF (2013) A three-dimensional atomistic-based process zone model simulation of fragmentation in polycrystalline solids. Int J Numer Methods Eng 93:989–1014CrossRefMathSciNetGoogle Scholar
  25. 25.
    Liu WK, Jun S, Zhang YF (1995) Reproducing kernel particle methods. Int J Numer Methods Fluids 20:1081–1106Google Scholar
  26. 26.
    Ren B, Li SF (2010) Meshfree simulations of plugging failures in high-speed impacts. Comput Struct 88:909–923CrossRefGoogle Scholar
  27. 27.
    Liu WK, Hao S, Belytschko T, Li S, Chang CT (2000) Multi-scale methods. Int J Numer Methods Eng 47(7): 1343–1361Google Scholar
  28. 28.
    Chen X, Gunzburger M (2011) Continuous and discontinuous finite element methods for a peridynamics model of mechanics. Comput Methods Appl Mech Eng 200:1237C1250Google Scholar
  29. 29.
    Li S, Liu WK (2004) Meshfree particle methods. Springer, BerlinzbMATHGoogle Scholar
  30. 30.
    von Neumman J, Richtmyer RD (1950) A method for the numerical calculation of hydrodynamic shocks. J Appl Phys 21:232–247Google Scholar
  31. 31.
    Monaghan JJ (1989) On the problem of penetration in particle methods. J Computat Phys 82:1–15CrossRefzbMATHGoogle Scholar
  32. 32.
    Ren B, Li SF (2012) Modeling and simulation of large-scale ductile fracture in plates and shells. Int J Solids Struct 49:2373–2393CrossRefMathSciNetGoogle Scholar
  33. 33.
    Bessa MA, Foster JT, Belytschko T, Liu WK (2014) A meshfree unification: reproducing kernel peridynamics. Computat Mech 53(6):1251–1264CrossRefzbMATHMathSciNetGoogle Scholar
  34. 34.
    Li S, Liu WK (1999) Reproducing kernel hierarchical partition of unity Part I—formulation and theory. Int J Numer Methods Eng 45(3):251–288Google Scholar
  35. 35.
    Libersky LD, Petscheck AG, Carney TC, Hipp JR, Allahdadi FA (1993) High strain Lagrangian hydrodynamics—a three dimensinoal SPH code for dynamic material response. J Computat Phys 109:67–75CrossRefzbMATHGoogle Scholar
  36. 36.
    Monaghan JJ (1994) Simulating free surface flow with SPH. J Computat Phys 110(2):399–406CrossRefzbMATHGoogle Scholar
  37. 37.
    Campbell PM (1988) Some new algorithms for boundary values problems in smoothed particle hydrodynamics. Defence Nuclear Agency (DNA) report DNA-88-286Google Scholar
  38. 38.
    Torres LQ (2012) Assessment of the applicability of nonlinear Drucker–Prager model with cap to adobe. 15th world conference on earthquake engineering (WCEE), Lisboa, PortugalGoogle Scholar
  39. 39.
    Han LH, Elliott JA, Bentham AC, Mills A, Amidon GE, Hancock BC (2008) A modified Drucker–Prager cap model for die compaction simulation of pharmaceutical powders. Int J Solids Struct 45:3088–3106CrossRefzbMATHGoogle Scholar
  40. 40.
    Zienkiewicz OC, Chan AHC, Pastor M, Schrefler BA, Shiomi T (1999) Computational geomechanics with special reference to earthquake engineering. Wiley, Chichester, UKzbMATHGoogle Scholar
  41. 41.
    Hughes TJR, Winget J (1980) Finite rotation effects in numerical integration of rate constitutive equations arising in large-deformation analysis. Int J Numer Methods Eng 15(12):1862–1867Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Bo Ren
    • 1
  • Houfu Fan
    • 1
  • Guy L. Bergel
    • 1
  • Richard A. Regueiro
    • 2
  • Xin Lai
    • 3
  • Shaofan Li
    • 1
    Email author
  1. 1.Department of Civil and Environmental EngineeringUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of Civil, Environmental, and Architectural EngineeringUniversity of Colorado at BoulderBoulderUSA
  3. 3.Department of Engineering Structure and MechanicsWuhan University of TechnologyWuhanChina

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