Skip to main content
SpringerLink
Log in

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

  • Original Paper
  • Published:
Computational Mechanics Aims and scope Submit manuscript

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.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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

Similar content being viewed by others

References

  1. Madenci E, Oterkus E (2014) Peridynamic theory and its applications. Springer, New York

    Book  MATH  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  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 176:215–222

    Article  Google Scholar 

  4. Gerstle W, Sau N, Silling S (2007) Peridynamics modeling of concrete structures. Nucl Eng Des 237:1250–1258

    Article  Google Scholar 

  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-2006-88

  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-2006-2267

  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 197–205

  8. Silling SA, Epton M, Weckner O, Xu J, Askari E (2007) Peridynamics states and constitutive modeling. J Elast 88:151–184

    Article  MATH  MathSciNet  Google Scholar 

  9. Silling SA, Lehoucq RB (2008) Convergence of peridynamics to classical elasticity theory. J Elast 93:13–37

    Article  MATH  MathSciNet  Google Scholar 

  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 263:20C26

    Article  MathSciNet  Google Scholar 

  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):1186–1195

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  13. Wecknera O, Mohamed NAN (2009) Viscoelastic material models in peridynamics. Appl Math Computat 219(11):6039–6043

    Article  Google Scholar 

  14. Tuniki BK (2012) Peridynamics constitutive model for concrete. Master thesis, Dept. of Civil Engineering, University of New Mexico, NM USA

  15. Vermeer PA, Borst R (1984) Non-associated plasticity for soils, concrete, and rock. Heron 29(3):3–64

    Google Scholar 

  16. Matsuoka H, Nakai T (1974) Stress-deformation and strength characteristics of soil under three different principal stresses. Proc Jpn Soc Civil Eng 232:59–70

    Article  Google Scholar 

  17. Drucker DC, Prager W (1952) Soil mechanics and plastic analysis or limit design. Quart Appl Math 10(2):157–165

    MATH  MathSciNet  Google Scholar 

  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 1467–1470

  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, TX

  20. Alia A, Souli M (2006) High explosive simulation using multi-material formulations. Appl Therm Eng 26:1032C1042

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  22. Liu GR, Liu MB (2003) Smoothed particle hydrodynamics: a meshfree particle method. World Scientific, Singapore

    Book  Google Scholar 

  23. Belytschko T, Liu WK, Moran B (2000) Nonlinear finite elements for continua and structures. Wiley, Chichester, UK

  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 93:989–1014

    Article  MathSciNet  Google Scholar 

  25. Liu WK, Jun S, Zhang YF (1995) Reproducing kernel particle methods. Int J Numer Methods Fluids 20:1081–1106

  26. Ren B, Li SF (2010) Meshfree simulations of plugging failures in high-speed impacts. Comput Struct 88:909–923

    Article  Google Scholar 

  27. Liu WK, Hao S, Belytschko T, Li S, Chang CT (2000) Multi-scale methods. Int J Numer Methods Eng 47(7): 1343–1361

  28. Chen X, Gunzburger M (2011) Continuous and discontinuous finite element methods for a peridynamics model of mechanics. Comput Methods Appl Mech Eng 200:1237C1250

  29. Li S, Liu WK (2004) Meshfree particle methods. Springer, Berlin

    MATH  Google Scholar 

  30. von Neumman J, Richtmyer RD (1950) A method for the numerical calculation of hydrodynamic shocks. J Appl Phys 21:232–247

  31. Monaghan JJ (1989) On the problem of penetration in particle methods. J Computat Phys 82:1–15

    Article  MATH  Google Scholar 

  32. Ren B, Li SF (2012) Modeling and simulation of large-scale ductile fracture in plates and shells. Int J Solids Struct 49:2373–2393

    Article  MathSciNet  Google Scholar 

  33. Bessa MA, Foster JT, Belytschko T, Liu WK (2014) A meshfree unification: reproducing kernel peridynamics. Computat Mech 53(6):1251–1264

    Article  MATH  MathSciNet  Google Scholar 

  34. Li S, Liu WK (1999) Reproducing kernel hierarchical partition of unity Part I—formulation and theory. Int J Numer Methods Eng 45(3):251–288

  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 109:67–75

    Article  MATH  Google Scholar 

  36. Monaghan JJ (1994) Simulating free surface flow with SPH. J Computat Phys 110(2):399–406

    Article  MATH  Google Scholar 

  37. Campbell PM (1988) Some new algorithms for boundary values problems in smoothed particle hydrodynamics. Defence Nuclear Agency (DNA) report DNA-88-286

  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, Portugal

  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 45:3088–3106

    Article  MATH  Google Scholar 

  40. Zienkiewicz OC, Chan AHC, Pastor M, Schrefler BA, Shiomi T (1999) Computational geomechanics with special reference to earthquake engineering. Wiley, Chichester, UK

    MATH  Google Scholar 

  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):1862–1867

Download references

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.

Author information

Authors and Affiliations

  1. Department of Civil and Environmental Engineering, University of California, Berkeley, CA, 94720, USA

    Bo Ren, Houfu Fan, Guy L. Bergel & Shaofan Li

  2. Department of Civil, Environmental, and Architectural Engineering, University of Colorado at Boulder, Boulder, CO, 80309, USA

    Richard A. Regueiro

  3. Department of Engineering Structure and Mechanics, Wuhan University of Technology, Wuhan, 430070, China

    Xin Lai

Authors
  1. Bo Ren
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Houfu Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guy L. Bergel
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Richard A. Regueiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Xin Lai
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Shaofan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shaofan Li.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Ren, B., Fan, H., Bergel, G.L. et al. A peridynamics–SPH coupling approach to simulate soil fragmentation induced by shock waves. Comput Mech 55, 287–302 (2015). https://doi.org/10.1007/s00466-014-1101-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00466-014-1101-6

Keywords

Search

Navigation