Skip to main content
SpringerLink
Log in

Simulations of single and double shock experiments using generalized interpolation material point method with a noise control strategy

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

Abstract

This paper presents an elaborated discussion on numerically handling single and double shock problems via the implementation of a meshless method, namely the generalized interpolation material point (GIMP) method. Oxygen-free high thermal conductivity copper and aluminum materials were considered. The capability of GIMP to accurately simulate such type of shock wave propagation problem is demonstrated and discussed via the 2-D plane strain solid mechanics formulation. GIMP is a modified material point method (MPM) that has been developed as an excellent numerical tool to solve dynamic problems involving large deformation, penetration, and fragmentation. However, double-flyer impact problem has rarely been simulated by using such a meshless method tool. In this work, the development and implementation of a set of well-tuned parameters are presented for modeling and analysis of both single and double shock experiments. Several procedures, including the discretization effect, were first performed within the GIMP framework to simulate single-flyer impact. Along with a modified update-strain-last method and an elastoplastic Johnson–Cook strength constitutive model, it is observed that the numerical results could be hugely improved when such a full mass matrix noise control strategy was utilized with optimized parameters for the numerical noise control. Thus, large oscillations that occur at the contact interface during high-speed impact can be smeared out without losing significant wave propagation features. Mie–Grüneisen equation of state was introduced to accurately identify the pressure-related shock-induced properties. Artificial defined explicit crack was introduced to model the spall and recompact in double-flyer impact. The simulation results of double-flyer impact problems, including free surface velocity, internal stress, and shock wave propagation presented via spatial–temporal diagrams, were shown to be in good agreement with previously reported data from experiments, finite element method, and analytical calculations.

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

Similar content being viewed by others

References

  1. Curran DR, Seaman L, Shockey DA (1977) Dynamic failure in solids. Phys Today 30:46–55. https://doi.org/10.1063/1.3037367

    Article  Google Scholar 

  2. Johnson JN (1981) Dynamic fracture and spallation in ductile solids. J Appl Phys 52:2812–2825. https://doi.org/10.1063/1.329011

    Article  Google Scholar 

  3. Zurek AK (1994) Spall experiments and microscopy of depleted U-0.75% Ti alloy. A Romanchenko correction to a spall strength calculation. J Nucl Mater 211:52–56. https://doi.org/10.1016/0022-3115(94)90280-1

    Article  Google Scholar 

  4. Yaziv D, Bless SJ, Rosenberg Z (1985) Study of spall and recompaction of ceramics using a double-impact technique. J Appl Phys 58:3415–3418. https://doi.org/10.1063/1.335759

    Article  Google Scholar 

  5. DeCarli PS, Meyers MA (1981) Design of Uniaxial strain shock recovery experiments. In: Meyers MA, Murr LE (eds) Shock waves and high-strain-rate Phenomena in Metals. Springer US, Boston, MA, pp 341–373

    Chapter  Google Scholar 

  6. Gray GT (1993) Influence of Shock-Wave deformation on the structure/property behavior of materials. In: Asay JR, Shahinpoor M (eds) High-pressure shock compression of solids. Springer, New York, pp 187–215

    Chapter  Google Scholar 

  7. Turley WD, Fensin SJ, Hixson RS et al (2018) Spall response of single-crystal copper. J Appl Phys 123:055102. https://doi.org/10.1063/1.5012267

    Article  Google Scholar 

  8. Hawkins MC, Thomas SA, Fensin SJ et al (2020) Spall and subsequent recompaction of copper under shock loading. J Appl Phys 128:045902. https://doi.org/10.1063/5.0011645

    Article  Google Scholar 

  9. Hixson RS (2004) Dynamic damage investigations using triangular waves. In: AIP conference proceedings. AIP, Portland, Oregon (USA), pp 469–472

  10. Koller DD Explosively Driven Shock Induced Damage in OFHC Copper. In: AIP Conference Proceedings. AIP, Baltimore (2006) Maryland (USA), pp 599–602

  11. Turley WD, Stevens GD, Hixson RS et al (2016) Explosive-induced shock damage in copper and recompression of the damaged region. J Appl Phys 120:085904. https://doi.org/10.1063/1.4962013

    Article  Google Scholar 

  12. Johnson GR, Cook WH (1985) Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures. Eng Fract Mech 21:31–48. https://doi.org/10.1016/0013-7944(85)90052-9

    Article  Google Scholar 

  13. Rajendran AM, Dietenberger MA, Grove DJ (1989) A void growth-based failure model to describe spallation. J Appl Phys 65:1521–1527. https://doi.org/10.1063/1.342967

    Article  Google Scholar 

  14. Rajendran AM, Grove DJ (1996) Modeling the shock response of silicon carbide, boron carbide and titanium diboride. Int J Impact Eng 18:611–631. https://doi.org/10.1016/0734-743X(96)89122-6

    Article  Google Scholar 

  15. Wang Z-P (1994) Void growth and compaction relations for ductile porous materials under intense dynamic general loading conditions. Int J Solids Struct 31:2139–2150. https://doi.org/10.1016/0020-7683(94)90194-5

    Article  MATH  Google Scholar 

  16. Zheng J, Wang Z-P (1995) Spall damage in aluminum alloy. Int J Solids Struct 32:1135–1148. https://doi.org/10.1016/0020-7683(94)00181-U

    Article  MATH  Google Scholar 

  17. Eftis J, Carrasco C, Osegueda R (2001) Simulations of hypervelocity impact damage and fracture of aluminum targets using a constitutive-microdamage material model. Int J Impact Eng 26:157–168. https://doi.org/10.1016/S0734-743X(01)00078-1

    Article  Google Scholar 

  18. Bar-on E, Rubin MB, Yankelevsky DZ (2003) Thermomechanical constitutive equations for the dynamic response of ceramics. Int J Solids Struct 40:4519–4548. https://doi.org/10.1016/S0020-7683(03)00211-7

    Article  MATH  Google Scholar 

  19. Butcher BM, Barker LM, Munson DE, Lundergan CD (1964) Influence of stress history on time-dependent spall in metals. AIAA J 2:977–990. https://doi.org/10.2514/3.2484

    Article  Google Scholar 

  20. Johnson GR, Stryk RA (1986) User instructions for the EPIC-2 code. Defense Systems Division, Edina, MN

    Google Scholar 

  21. Grove DJ, Rajendran AM, Dietenberger MA (1990) Numerical simulation of a double flyer impact experiment. In: Shock compression of condensed matter–1989: proceedings of the American Physical Society Topical Conference held in Albuquerque, New Mexico, 14–17 Aug 1989. Sole distributors for the USA and Canada, North-Holland, Elsevier, Amsterdam, pp 365–368

  22. Bodner SR, Partom Y (1975) Constitutive equations for Elastic-Viscoplastic strain-hardening materials. J Appl Mech 42:385–389. https://doi.org/10.1115/1.3423586

    Article  Google Scholar 

  23. Steffen M, Wallstedt PC, Guilkey JE et al (2008) Examination and analysis of implementation choices within the Material Point Method (MPM). CMES-Comput Model Eng Sci 31:107–128. https://doi.org/10.3970/cmes.2008.031.107

    Article  Google Scholar 

  24. Nairn JA, Hammerquist CC (2021) Material point method simulations using an approximate full mass matrix inverse. Comput Methods Appl Mech Eng 377:113667. https://doi.org/10.1016/j.cma.2021.113667

    Article  MathSciNet  MATH  Google Scholar 

  25. Nairn JA (2003) Material Point Method Calculations with Explicit Cracks. CMES-Comput Model Eng Sci 4:649–664. https://doi.org/10.3970/cmes.2003.004.649

    Article  MATH  Google Scholar 

  26. Sulsky D, Chen Z, Schreyer HL (1994) A particle method for history-dependent materials. Comput Methods Appl Mech Eng 118:179–196. https://doi.org/10.1016/0045-7825(94)90112-0

    Article  MathSciNet  MATH  Google Scholar 

  27. Harlow FH (1962) The particle-in-cell method for numerical solution of problems in fluid dynamics

  28. Brackbill JU, Ruppel HM (1986) FLIP: a method for adaptively zoned, particle-in-cell calculations of fluid flows in two dimensions. J Comput Phys 65:314–343. https://doi.org/10.1016/0021-9991(86)90211-1

    Article  MathSciNet  MATH  Google Scholar 

  29. Brackbill JU, Kothe DB, Ruppel HM (1988) Flip: a low-dissipation, particle-in-cell method for fluid flow. Comput Phys Commun 48:25–38. https://doi.org/10.1016/0010-4655(88)90020-3

    Article  Google Scholar 

  30. Hammerquist CC, Nairn JA (2017) A new method for material point method particle updates that reduces noise and enhances stability. Comput Methods Appl Mech Eng 318:724–738. https://doi.org/10.1016/j.cma.2017.01.035

    Article  MathSciNet  MATH  Google Scholar 

  31. Nairn JA (2015) Numerical simulation of orthogonal cutting using the material point method. Eng Fract Mech 149:262–275. https://doi.org/10.1016/j.engfracmech.2015.07.014

    Article  Google Scholar 

  32. de Vaucorbeil A, Nguyen VP, Sinaie S, Wu JY (2020) Material point method after 25 years: theory, implementation, and applications. Advances in Applied mechanics. Elsevier, pp 185–398

  33. Stomakhin A, Schroeder C, Chai L et al (2013) A material point method for snow simulation. ACM Trans Graph 32:1–10. https://doi.org/10.1145/2461912.2461948

    Article  MATH  Google Scholar 

  34. Bardenhagen SG, Kober EM (2004) The generalized interpolation material point method. CMES-Comput Model Eng Sci 5:477–496. https://doi.org/10.3970/cmes.2004.005.477

    Article  Google Scholar 

  35. Sadeghirad A, Brannon RM, Burghardt J (2011) A convected particle domain interpolation technique to extend applicability of the material point method for problems involving massive deformations: CONVECTED PARTICLE DOMAIN INTERPOLATION TECHNIQUE. Int J Numer Methods Eng 86:1435–1456. https://doi.org/10.1002/nme.3110

    Article  MATH  Google Scholar 

  36. Zhang DZ, Ma X, Giguere PT (2011) Material point method enhanced by modified gradient of shape function. J Comput Phys 230:6379–6398. https://doi.org/10.1016/j.jcp.2011.04.032

    Article  MathSciNet  MATH  Google Scholar 

  37. Vaucorbeil A, Hutchinson CR (2020) A new total-lagrangian smooth particle hydrodynamics approximation for the simulation of damage and fracture of ductile materials. Int J Numer Methods Eng 121:2227–2245. https://doi.org/10.1002/nme.6306

    Article  MathSciNet  Google Scholar 

  38. Graff KF (1991) Wave motion in elastic solids. Dover Publications, New York

    MATH  Google Scholar 

  39. Rajendran AM, Grove DJ, Dietenberger MA, Cook WH (1991) A dynamic failure model for Ductile materials. University of Dayton Research Institute, Dayton, OH

    Google Scholar 

  40. Bourne NK, Rosenberg Z (1999) Manganin gauge and VISAR histories in shock-stressed polymethylmethacrylate. Proc R Soc Lond Ser Math Phys Eng Sci 455:1259–1266. https://doi.org/10.1098/rspa.1999.0358

    Article  Google Scholar 

  41. Nairn JA, Hammerquist CC, Smith GD (2020) New material point method contact algorithms for improved accuracy, large-deformation problems, and proper null-space filtering. Comput Methods Appl Mech Eng 362:112859. https://doi.org/10.1016/j.cma.2020.112859

    Article  MathSciNet  MATH  Google Scholar 

  42. Yaziv D, Bless SJ (1984) Shock fracture and recompaction of copper. In: Army symposium on solid mechanics. Army Materials and Mechanics Research Center, Newport, RI, pp 329–332

Download references

Acknowledgements

The use of trade, product or firm names in this report is for descriptive purposes only and does not imply endorsement by the US Government. The tests described and the resulting data presented herein were obtained from research conducted under the Installations and Operational Environments Program of the United States Army Corps of Engineers – Engineer Research and Development Center. Permission was granted by the Chief of Engineers to publish this information. The findings of this report are not to be construed as an official Department of the Army position unless so designated by other authorized documents.  The authors (Huadian Zhang, A.M. Rajendran, and Shan Jiang) acknowledge the support from the U.S. Army Corp of Engineers - Engineering Research and Development Center (W912HZ2020042). The authors thank Professor John A. Nairn for his guidance in using uGIMP as well as for some very helpful discussions.

Author information

Authors and Affiliations

  1. Department of Mechanical Engineering, University of Mississippi, University, MS, 38677, USA

    Huadian Zhang, A. M. Rajendran & Shan Jiang

  2. Environmental Laboratory, U.S. Army Engineer Research and Development Center, Vicksburg, MS, 39180, USA

    Manoj K. Shukla

Authors
  1. Huadian Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manoj K. Shukla
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. M. Rajendran
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Shan Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Shan Jiang.

Ethics declarations

Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Publisher′s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary material 1 (DOCX 30 kb)

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, H., Shukla, M.K., Rajendran, A.M. et al. Simulations of single and double shock experiments using generalized interpolation material point method with a noise control strategy. Comp. Part. Mech. 10, 1795–1809 (2023). https://doi.org/10.1007/s40571-023-00590-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-023-00590-1

Keywords

Search

Navigation