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

  • Baochen ZhuEmail author
  • Ruoqiang Feng


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.


Discrete solid element model Spring stiffness Plasticity Fracture 



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.

Compliance with ethical standards

Conflict of interest

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


  1. 1.
    Moës Nicolas, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Meth Eng 46(1):131–150CrossRefzbMATHGoogle Scholar
  2. 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 60:131–151CrossRefGoogle Scholar
  3. 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 121:63–76CrossRefGoogle Scholar
  4. 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):270–277CrossRefGoogle Scholar
  5. 5.
    Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7:55–129MathSciNetCrossRefGoogle Scholar
  6. 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 300:347–374MathSciNetCrossRefGoogle Scholar
  7. 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 295:77–107MathSciNetCrossRefGoogle Scholar
  8. 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):1665–1682CrossRefGoogle Scholar
  9. 9.
    Remmers JJC, Borst RD, Needleman A (2003) A cohesive segments method for the simulation of crack growth. Comput Mech 31(1–2):69–77CrossRefzbMATHGoogle Scholar
  10. 10.
    Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65CrossRefGoogle Scholar
  11. 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):1497–1517CrossRefGoogle Scholar
  12. 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):4087–4100CrossRefzbMATHGoogle Scholar
  13. 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 108:98–114CrossRefGoogle Scholar
  14. 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 91:615–630CrossRefGoogle Scholar
  15. 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):2093–2101CrossRefGoogle Scholar
  16. 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):253–259CrossRefGoogle Scholar
  17. 17.
    Ma Y, Huang H (2018) Dem analysis of failure mechanisms in the intact brazilian test. Int J Rock Mech Min Sci 102:109–119CrossRefGoogle Scholar
  18. 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 87:120–131CrossRefGoogle Scholar
  19. 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):3787–3797CrossRefGoogle Scholar
  20. 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):244–253CrossRefGoogle Scholar
  21. 21.
    Hentz S, Daudeville L, Donzé FV (2004) Identification and validation of a discrete element model for concrete. J Eng Mech 130(6):709–719CrossRefGoogle Scholar
  22. 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 175:118–129CrossRefGoogle Scholar
  23. 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):936–953CrossRefGoogle Scholar
  24. 24.
    Liu L, Thornton C, Shaw SJ, Tadjouddine EM (2016) Discrete element modelling of agglomerate impact using autoadhesive elastic-plastic particles. Powder Technol 297:81–88CrossRefGoogle Scholar
  25. 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):383–400CrossRefGoogle Scholar
  26. 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):57–68Google Scholar
  27. 27.
    Zhu BC, Feng RQ, Wang X (2018) 3D discrete solid element method for elastoplastic problems of continuity. J Eng Mech 144(7):04018051CrossRefGoogle Scholar
  28. 28.
    Xu ZL (2006) Elastic mechanics. Higher Education Press, BeijingGoogle Scholar
  29. 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):2539–2575CrossRefzbMATHGoogle Scholar
  30. 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):37–44CrossRefGoogle Scholar
  31. 31.
    Mohammadi S, Forouzan-Sepehr S, Asadollahi A (2002) Contact based delamination and fracture analysis of composites. Thin-Walled Struct 40(7):595–609CrossRefGoogle Scholar
  32. 32.
    Seifi R, Kabiri AR (2013) Lateral load effects on buckling of cracked plates under tensile loading. Thin Wall Struct 72(10):37–47CrossRefzbMATHGoogle Scholar
  33. 33.
    Wu Tung-Yueh (2013) Dynamic nonlinear analysis of shell structures using a vector form intrinsic finite element. Eng Struct 56:2028–2040CrossRefGoogle Scholar
  34. 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):1396–1412CrossRefGoogle Scholar

Copyright information

© OWZ 2019

Authors and Affiliations

  1. 1.The Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, School of Civil EngineeringSoutheast UniversityNanjingChina

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