Skip to main content
SpringerLink
Log in

Discrete solid element model applied to plasticity and dynamic crack propagation in continuous medium

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

Abstract

In this work, the discrete solid element model (DSEM) applied to plasticity and dynamic crack propagation problems in the continuous medium is developed and implemented. First, the Drucker’s postulate and the consistency condition are used to establish the plastic flow rule in the DSEM. The plastic scale factor which characterizes the plastic displacement increment of spherical elements is derived by the classical plastic mechanics. The elastoplastic contact constitutive equations of the strain-hardening material are established, which can be used for elasticity, unloading and loading. Second, to accurately simulate the mechanical behavior of continuity, the spring stiffness of spherical elements on the boundary of the DSEM is strictly deduced using the principle of conservation of energy, and the relationship between the spring stiffness and the continuous constitutive parameters is established. Third, the bilinear contact softening model is adopted to simulate the crack propagation in the continuous medium. The criteria for the crack propagation based on the fracture energy of the material are developed. The numerical examples are presented to show the capability and effectiveness of the DSEM in simulating the dynamic buckling and crack propagation problems. The obtained results are in agreement with experimental and numerical results published by other researchers.

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
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28

Similar content being viewed by others

References

  1. Moës Nicolas, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Meth Eng 46(1):131–150

    Article  MathSciNet  MATH  Google Scholar 

  2. Lal A, Palekar SP, Mulani SB, Kapania RK (2017) Stochastic extended finite element implementation for fracture analysis of laminated composite plate with a central crack. Aerosp Sci Technol 60:131–151

    Article  Google Scholar 

  3. Asareh I, Yoon YC, Song JH (2018) A numerical method for dynamic fracture using the extended finite element method with non-nodal enrichment parameters. Int J Impact Eng 121:63–76

    Article  Google Scholar 

  4. Lancaster IM, Khalid HA, Kougioumtzoglou IA (2013) Extended FEM modelling of crack propagation using the semi-circular bending test. Constr Build Mater 48(11):270–277

    Article  Google Scholar 

  5. Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7:55–129

    Article  MathSciNet  Google Scholar 

  6. Ferté G, Massin P, Moës N (2016) 3d crack propagation with cohesive elements in the extended finite element method. Comput Methods Appl Mech Eng 300:347–374

    Article  MathSciNet  MATH  Google Scholar 

  7. Wu JY, Li FB (2015) An improved stable XFEM (Is-XFEM) with a novel enrichment function for the computational modeling of cohesive cracks. Comput Methods Appl Mech Eng 295:77–107

    Article  MathSciNet  MATH  Google Scholar 

  8. Turon A, Dávila CG, Camanho PP, Costa J (2007) An engineering solution for mesh size effects in the simulation of delamination using cohesive zone models. Eng Fract Mech 74(10):1665–1682

    Article  Google Scholar 

  9. Remmers JJC, Borst RD, Needleman A (2003) A cohesive segments method for the simulation of crack growth. Comput Mech 31(1–2):69–77

    Article  MATH  Google Scholar 

  10. Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65

    Article  Google Scholar 

  11. Rojek J, Labra C, Su O, Oñate E (2012) Comparative study of different discrete element models and evaluation of equivalent micromechanical parameters. Int J Solids Struct 49(13):1497–1517

    Article  Google Scholar 

  12. Liao CL, Chang TP, Young DH, Chang CS (1997) Stress-strain relationship for granular materials based on the hypothesis of best fit. Int J Solids Struct 34(31–32):4087–4100

    Article  MATH  Google Scholar 

  13. Leclerc W, Haddad H, Guessasma M (2016) On the suitability of a discrete element method to simulate cracks initiation and propagation in heterogeneous media. Int J Solids Struct 108:98–114

    Article  Google Scholar 

  14. Le BD, Dau F, Charles JL, Iordanoff I (2016) Modeling damages and cracks growth in composite with a 3D discrete element method. Compos B 91:615–630

    Article  Google Scholar 

  15. Sheng Y, Yang DM, Tan YQ, Ye JQ (2010) Microstructure effects on transverse cracking in composite laminae by DEM. Compos Sci Technol 70(14):2093–2101

    Article  Google Scholar 

  16. Yang D, Sheng Y, Ye J, Tan Y (2010) Discrete element modeling of the microbond test of fiber reinforced composite. Comput Mater Sci 49(2):253–259

    Article  Google Scholar 

  17. Ma Y, Huang H (2018) Dem analysis of failure mechanisms in the intact brazilian test. Int J Rock Mech Min Sci 102:109–119

    Article  Google Scholar 

  18. Koteski L, Iturrioz I, Cisilino AP, D’Ambra RB, Pettarin V, Fasce L et al (2016) A lattice discrete element method to model the falling-weight impact test of PMMA specimens. Int J Impact Eng 87:120–131

    Article  Google Scholar 

  19. Braun M, Fernández-Sáez J (2014) A new 2D discrete model applied to dynamic crack propagation in brittle materials. Int J Solids Struct 51(21–22):3787–3797

    Article  Google Scholar 

  20. Sinaie S (2017) Application of the discrete element method for the simulation of size effects in concrete samples. Int J Solids Struct 108(1):244–253

    Article  Google Scholar 

  21. Hentz S, Daudeville L, Donzé FV (2004) Identification and validation of a discrete element model for concrete. J Eng Mech 130(6):709–719

    Article  Google Scholar 

  22. Guo Y, Wassgren C, Curtis JS, Xu D, Guo Y, Wassgren C et al (2017) A bonded sphero-cylinder model for the discrete element simulation of elasto-plastic fibers. Chem Eng Sci 175:118–129

    Article  Google Scholar 

  23. Zhang Y, Mabrouki T, Nelias D, Courbon C, Rech J, Gong Y (2012) Cutting simulation capabilities based on crystal plasticity theory and discrete cohesive elements. J Mater Process Technol 212(4):936–953

    Article  Google Scholar 

  24. Liu L, Thornton C, Shaw SJ, Tadjouddine EM (2016) Discrete element modelling of agglomerate impact using autoadhesive elastic-plastic particles. Powder Technol 297:81–88

    Article  Google Scholar 

  25. Thakur SC, Morrissey JP, Sun J, Chen JF, Ooi JY (2014) Micromechanical analysis of cohesive granular materials using the discrete element method with an adhesive elasto-plastic contact model. Granul Matter 16(3):383–400

    Article  Google Scholar 

  26. Wei HU, Jin F, Zhang C, Wang J (2012) 3D mode discrete element method with the elastoplastic model. Front Struct Civ Eng 6(1):57–68

    Google Scholar 

  27. Zhu BC, Feng RQ, Wang X (2018) 3D discrete solid element method for elastoplastic problems of continuity. J Eng Mech 144(7):04018051

    Article  Google Scholar 

  28. Xu ZL (2006) Elastic mechanics. Higher Education Press, Beijing

    Google Scholar 

  29. Jefferson G, Haritos GK, Mcmeeking RM (2002) The elastic response of a cohesive aggregate—a discrete element model with coupled particle interaction. J Mech Phys Solids 50(12):2539–2575

    Article  MATH  Google Scholar 

  30. Sun Y, Pugno N, Gong B, Ding Q (2015) A simplified hardening cohesive zone model for bondline thickness dependence on adhesive joints. Int J Fract 194(1):37–44

    Article  Google Scholar 

  31. Mohammadi S, Forouzan-Sepehr S, Asadollahi A (2002) Contact based delamination and fracture analysis of composites. Thin-Walled Struct 40(7):595–609

    Article  Google Scholar 

  32. Seifi R, Kabiri AR (2013) Lateral load effects on buckling of cracked plates under tensile loading. Thin Wall Struct 72(10):37–47

    Article  MATH  Google Scholar 

  33. Wu Tung-Yueh (2013) Dynamic nonlinear analysis of shell structures using a vector form intrinsic finite element. Eng Struct 56:2028–2040

    Article  Google Scholar 

  34. So H, Chen JT (2007) Experimental study of dynamic crushing of thin plates stiffened by stamping with v-grooves. Int J Impact Eng 34(8):1396–1412

    Article  Google Scholar 

Download references

Acknowledgements

This research was financial supported by the Fundamental Research Funds for the Central Universities, by the Colleges and Universities in Jiangsu Province Plans to Graduate Research and Innovation (KYLX15_0089), by a project funded by the Priority Academic Program Development of the Jiangsu Higher Education Institutions and by the Natural Science Foundation of China under Grant Number 51538002.

Author information

Authors and Affiliations

  1. The Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, School of Civil Engineering, Southeast University, Nanjing, 210096, China

    Baochen Zhu & Ruoqiang Feng

Authors
  1. Baochen Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ruoqiang Feng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Baochen Zhu.

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

Zhu, B., Feng, R. Discrete solid element model applied to plasticity and dynamic crack propagation in continuous medium. Comp. Part. Mech. 6, 611–627 (2019). https://doi.org/10.1007/s40571-019-00237-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-019-00237-0

Keywords

Search

Navigation