Skip to main content
SpringerLink
Log in

Inelastic peridynamic model for molecular crystal particles

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

Abstract

The peridynamic theory of solid mechanics is applied to modeling the deformation and fracture of micrometer-sized particles made of organic crystalline material. A new peridynamic material model is proposed to reproduce the elastic–plastic response, creep, and fracture that are observed in experiments. The model is implemented in a three-dimensional, meshless Lagrangian simulation code. In the small deformation, elastic regime, the model agrees well with classical Hertzian contact analysis for a sphere compressed between rigid plates. Under higher load, material and geometrical nonlinearity is predicted, leading to fracture. The material parameters for the energetic material CL-20 are evaluated from nanoindentation test data on the cyclic compression and failure of micrometer-sized grains.

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

Similar content being viewed by others

References

  1. Barr C, Cooper M, Lechman J, Bufford DC. The mechanical response of individual micron-sized molecular crystal particles (in preparation)

  2. Behzadinasab M, Vogler TJ, Peterson AM, Rahman R, Foster JT (2018) Peridynamics modeling of a shock wave perturbation decay experiment in granular materials with intra-granular fracture. J Dyn Behav Mater 4:529–542

    Article  Google Scholar 

  3. Benson DJ (1994) An analysis by direct numerical simulation of the effects of particle morphology on the shock compaction of copper powder. Modell Simul Mater Sci Eng 2:535

    Article  Google Scholar 

  4. Bobaru F (2007) Influence of van der Waals forces on increasing the strength and toughness in dynamic fracture of nanofibre networks: a peridynamic approach. Modell Simul Mater Sci Eng 15:397–417

    Article  Google Scholar 

  5. Chen H (2018) Bond-associated deformation gradients for peridynamic correspondence model. Mech Res Commun 90:34–41

    Article  Google Scholar 

  6. Courant R, Friedrichs K, Lewy H (1928) Über die partiellen differenzengleichungen der mathematischen physik. Math Ann 100:32–74

    Article  MathSciNet  Google Scholar 

  7. De Meo D, Zhu N, Oterkus E (2016) Peridynamic modeling of granular fracture in polycrystalline materials. J Eng Mater Technol 138:041008

    Article  Google Scholar 

  8. Diehl P, Prudhomme S, Lévesque M (2019) A review of benchmark experiments for the validation of peridynamics models. J Peridynamics Nonlocal Modeling 1:14–35

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  10. Hertz H (1882) Über die Berührung fester elastischer Körper. J. Rein. Angew. Math. 92:156–171

    MATH  Google Scholar 

  11. Kamensky D, Behzadinasab M, Foster JT, Bazilevs Y (2019) Peridynamic modeling of frictional contact. J Peridynamics Nonlocal Modeling 1:1–15

    Article  MathSciNet  Google Scholar 

  12. Kildashti K, Dong K, Samali B, Zheng Q, Yu A (2018) Evaluation of contact force models for discrete modelling of ellipsoidal particles. Chem Eng Sci 177:1–17

    Article  Google Scholar 

  13. Lammi CJ, Vogler TJ (2012) Mesoscale simulations of granular materials with peridynamics. AIP Conf Proc 1426:1467–1470

    Article  Google Scholar 

  14. Lammi CJ, Vogler TJ (2014) A nonlocal peridynamic plasticity model for the dynamic flow and fracture of concrete. Sandia National Laboratories (SNL-CA), Livermore, CA (United States)

  15. Le VD, Gratton M, Caliez M, Frachon A, Picart D (2010) Experimental mechanical characterization of plastic-bonded explosives. J Mater Sci 45:5802–5813

    Article  Google Scholar 

  16. Li C, Wan M, Wu X-D, Huang L (2010) Constitutive equations in creep of 7b04 aluminum alloys. Mater Sci Eng A 527:3623–3629

    Article  Google Scholar 

  17. Macek RW, Silling SA (2007) Peridynamics via finite element analysis. Finite Elem Anal Des 43:1169–1178

    Article  MathSciNet  Google Scholar 

  18. Madenci E, Oterkus E (2013) Peridynamic theory and its applications. Springer, New York

    MATH  Google Scholar 

  19. Mitchell JA (2011) A non-local, ordinary-state-based viscoelasticity model for peridynamics. Technical report SAND2011-8064, Sandia National Laboratories, Albuquerque, New Mexico 87185 and Livermore, California 94550

  20. Olsson E, Larsson P-L (2013) A numerical analysis of cold powder compaction based on micromechanical experiments. Powder Technol 243:71–78

    Article  Google Scholar 

  21. Olsson E, Larsson P-L (2015) Micromechanical investigation of the fracture behavior of powder materials. Powder Technol 286:288–302

    Article  Google Scholar 

  22. Popov VL, Hess M, Willert E (2009) Handbook of contact mechanics. Springer, Berlin

    MATH  Google Scholar 

  23. Ransing R, Gethin D, Khoei A, Mosbah P, Lewis R (2000) Powder compaction modelling via the discrete and finite element method. Mater Des 21:263–269

    Article  Google Scholar 

  24. Seleson P, Parks M (2011) On the role of the influence function in the peridynamic theory. Int J Multiscale Comput Eng 9:689–706

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  28. Silling SA, Lehoucq RB (2010) The peridynamic theory of solid mechanics. Adv Appl Mech 44:73–166

    Article  Google Scholar 

  29. Storåkers B, Fleck NA, McMeeking RM (1999) The viscoplastic compaction of composite powders. J Mech Phys Solids 47:785–815

    Article  Google Scholar 

  30. Sun S, Sundararaghavan V (2014) A peridynamic implementation of crystal plasticity. Int J Solids Struct 51:3350–3360

    Article  Google Scholar 

  31. Sun T, Xiao JJ, Liu Q, Zhao F, Xiao HM (2014) Comparative study on structure, energetic and mechanical properties of a \(\varepsilon \)-cl-20/hmx cocrystal and its composite with molecular dynamics simulation. J Mater Chem A 2:13898–13904

    Article  Google Scholar 

  32. Tavares L, King R (2002) Modeling of particle fracture by repeated impacts using continuum damage mechanics. Powder Technol 123(2–3):138–146

    Article  Google Scholar 

  33. Warren TL, Silling SA, Askari A, Weckner O, Epton MA, Xu J (2009) A non-ordinary state-based peridynamic method to model solid material deformation and fracture. Int J Solids Struct 46:1186–1195

    Article  Google Scholar 

  34. Zhu F, Zhao J (2018) A peridynamic investigation on crushing of sand particles. Géotechnique 69:526–540

    Article  Google Scholar 

  35. Zhu F, Zhao J (2019) Modeling continuous grain crushing in granular media: a hybrid peridynamics and physics engine approach. Comput Methods Appl Mech Eng 348:334–355

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was performed under a Laboratory Directed Research and Development (LDRD) project at Sandia National Laboratories. Sandia National Laboratories is a multimission 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. This paper describes objective technical results and analysis. Any subjective views or opinions that might be expressed in the paper do not necessarily represent the views of the U.S. Department of Energy or the United States Government.

Author information

Authors and Affiliations

  1. Sandia National Laboratories, Albuquerque, NM, 87185, USA

    Stewart A. Silling, Christopher Barr, Marcia Cooper, Jeremy Lechman & Daniel C. Bufford

Authors
  1. Stewart A. Silling
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Christopher Barr
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marcia Cooper
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jeremy Lechman
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Daniel C. Bufford
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stewart A. Silling.

Ethics declarations

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Publisher's Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Silling, S.A., Barr, C., Cooper, M. et al. Inelastic peridynamic model for molecular crystal particles. Comp. Part. Mech. 8, 1005–1017 (2021). https://doi.org/10.1007/s40571-021-00389-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-021-00389-y

Keywords

Search

Navigation