Skip to main content
Log in

On the suitability of a 3D discrete element method to model the composite damage induced by thermal expansion mismatch

  • Published:
Computational Particle Mechanics Aims and scope Submit manuscript

Abstract

The paper aims to investigate the suitability of a 3D discrete element method to simulate the thermal-induced damage in composite materials using a cohesive beam model. First, we aim to predict the elastic behavior of continuous material in the case of a homogeneous medium. For that purpose, mechanical tests are performed on a representative pattern and some properties of continuous materials are discussed. Then, we investigate a model of thermal expansion in the context of a homogeneous material to simulate its thermoelastic behavior. The case of a single-inclusion composite is also discussed and some comparisons are done with the finite element method (FEM) and analytical formulations. Damage effects and interfacial debonding are taken into account in order to model the thermal-induced damage due to the thermal expansion mismatch. Finally, a similar study is applied in the context of multi-inclusion composite. From a quantitative standpoint, discrete element results in terms of coefficient of thermal expansion and stress and strain fields are in good agreement with the predictions given by FEM and analytical formulations. Besides, from a qualitative standpoint, the present work exhibits suitable damage modes in accordance with thermal conditions.

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

Access this article

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

Instant access to the full article PDF.

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
Fig. 29
Fig. 30

Similar content being viewed by others

References

  1. Krüger R (2002) The virtual crack closure technique: history, approach and applications. Appl Mech Rev 57:109–143

    Article  Google Scholar 

  2. Xu X-P, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42(9):1397–1434

    Article  MATH  Google Scholar 

  3. Zhang Z, Paulino GH (2005) Cohesive zone modeling of dynamic failure in homogeneous and functionally graded materials. Int J Plast 21(6):1195–1254

    Article  MATH  Google Scholar 

  4. Liu X, Duddu R, Waisman H (2012) Discrete damage zone model for fracture initiation and propagation. Eng Fract Mech 92:1–18

    Article  Google Scholar 

  5. Moes N, Dolbow J, Belytschko T (1999) A finite element method for crack growth without remeshing. Int J Numer Methods Eng 46:131–150

    Article  MathSciNet  MATH  Google Scholar 

  6. Rabczuk T, Belytschko T (2007) A three-dimensional large deformation meshfree method for arbitrary evolving cracks. Comput Methods Appl Mech Eng 196(29):2777–2799

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  8. Nicot F, Hadda N, Guessasma M, Fortin J, Millet O (2013) On the definition of the stress tensor in granular media. Int J Solids Struct 50:2508–2517

    Article  Google Scholar 

  9. Fillot N, Iordanoff I, Berthier Y (2007) Modelling third body flows with a discrete element method—a tool for understanding wear with adhesive particles. Tribol Int 40(6):973–981

    Article  Google Scholar 

  10. Machado C, Guessasma M, Bellenger E (2015) Electromechanical modeling by dem for assessing internal ball bearing loading. Mech Mach Theory 92:338–355

    Article  Google Scholar 

  11. Machado C, Guessasma M, Bourny V (2018) Electromechanical prediction of the regime of lubrication in ball bearings using discrete element method. Tribol Int 127:69–83

    Article  Google Scholar 

  12. Sanni I, Bellenger E, Fortin J, Coorevits P (2010) A reliable algorithm to solve 3D frictional multi-contact problems: application to granular media. J Comput Appl Math 4:1161–1171

    Article  MathSciNet  MATH  Google Scholar 

  13. Chen I-W (2000) Grain boundary kinetics in oxide ceramics with the cubic fluorite crystal structure and its derivatives. Interface Sci 8(2):147–156

    Article  Google Scholar 

  14. Pizette P, Martin CL, Delette G, Sornay P, Sans F (2010) Compaction of aggregated ceramic powders: from contact laws to fracture and yield surfaces. Powder Technol 198(2):240–250

    Article  Google Scholar 

  15. Liu X, Hu Z, Wu W, Zhan J, Herz F, Specht E (2017) Dem study on the surface mixing and whole mixing of granular materials in rotary drums. Powder Technol 315:438–444

    Article  Google Scholar 

  16. Haddad H, Guessasma M, Fortin J (2014) Heat transfer by conduction using DEM–FEM coupling method. Comput Mater Sci 81:339–347

    Article  Google Scholar 

  17. Terreros I, Iordanoff I, Charles JL (2013) Simulation of continuum heat conduction using DEM domains. Comput Mater Sci 69:46–52

    Article  Google Scholar 

  18. Jebahi M, André D, Dau F, Charles J l, Iordanoff I (2013) Simulation of vickers indentation of silica glass. J Non-Cryst Solids 378:15–24

    Article  Google Scholar 

  19. Ben Dhia H, Rateau G (2005) The Arlequin method as a flexible engineering design tool. Int J Numer Methods Eng 62(11):1442–1462

    Article  MATH  Google Scholar 

  20. Potyondy DO, Cundall PA (2004) A bonded-particle model for rock. Int J Rock Mech Min Sci 41(8):1329–1364

    Article  Google Scholar 

  21. Schlangen E, Garboczi EJ (1996) New method for simulating fracture using an elastically uniform random geometry lattice. Int J Eng Sci 34(10):1131–1144

    Article  MATH  Google Scholar 

  22. André D, Iordanoff I, Charles JL, Néauport J (2012) Discrete element method to simulate continuous material by using the cohesive beam model. Comput Methods Appl Mech Eng 213–216:113–125

    Article  MATH  Google Scholar 

  23. Leclerc W (2017) Discrete element method to simulate the elastic behavior of 3D heterogeneous continuous media. Int J Solids Struct 121:86–102

    Article  Google Scholar 

  24. André D, Levraut B, Tessier-Doyen N, Huger M (2017) A discrete element thermo-mechanical modelling of diffuse damage induced by thermal expansion mismatch of two-phase materials. Comput Methods Appl Mech Eng 318:898–916

    Article  MathSciNet  MATH  Google Scholar 

  25. Leclerc W, Haddad H, Guessasma M (2018) On a discrete element method to simulate thermal-induced damage in 2D composite materials. Comput Struct 196:277–291

    Article  Google Scholar 

  26. Tan Y, Yang D, Sheng Y (2009) Discrete element method modeling of fracture and damage in the machining process of polycrystalline sic. J Eur Ceram Soc 29(6):1029–1037

    Article  Google Scholar 

  27. Maheo L, Dau F, André D, Charles JL, Iordanoff I (2015) A promising way to model cracks in composite using discrete element method. Compos B Eng 71:193–202

    Article  Google Scholar 

  28. Chen Z, Jin X, Wang M (2018) A new thermo-mechanical coupled dem model with non-spherical grains for thermally induced damage of rocks. J Mech Phys Solids 116:54–69

    Article  MathSciNet  Google Scholar 

  29. Rojek J, Oñate E, Labra C, Kargl H (2011) Discrete element simulation of rock cutting. Int J Rock Mech Min Sci 48(6):996–1010

    Article  Google Scholar 

  30. Hentz S, Donzé FV, Daudeville L (2004) Discrete element modelling of concrete submitted to dynamic loading at high strain rates. Comput Struct 82(29):2509–2524

    Article  Google Scholar 

  31. Sinaie S, Heidarpour A, Zhao XL (2016) A micro-mechanical parametric study on the strength degradation of concrete due to temperature exposure using the discrete element method. Int J Solids Struct 88–89:165–177

    Article  Google Scholar 

  32. Radi K, Jauffrès D, Deville S, Martin CL (2019) Elasticity and fracture of brick and mortar materials using discrete element simulations. J Mech Phys Solids 126:101–116

    Article  MathSciNet  Google Scholar 

  33. Schlangen E, Garboczi EJ (1997) Fracture simulations of concrete using lattice models: computational aspects. Eng Fract Mech 57(2):319–332

    Article  Google Scholar 

  34. André D, Jebahi M, Iordanoff I, Charles J-L, Néauport J (2013) Using the discrete element method to simulate brittle fracture in the indentation of a silica glass with a blunt indenter. Comput Methods Appl Mech Eng 265:136–147

    Article  MATH  Google Scholar 

  35. Leclerc W, Haddad H, Guessasma M (2017) 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 

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

    Article  Google Scholar 

  37. 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 

  38. Boccaccini AR, Chawla KK (1999) Damage development during thermal cycling of metal and glass matrix composites. Woodhead Publishing, Cambridge

    Google Scholar 

  39. Fu Y, Wong YL, Tang CA, Poon CS (2004) Thermal induced stress and associated cracking in cement-based composite at elevated temperatures—part II: thermal cracking around multiple inclusions. Cem Concr Compos 26:113–126

    Article  Google Scholar 

  40. Lu TC, Yang J, Suo Z, Evans AG, Hecht R, Mehrabian R (1991) Matrix cracking in intermetallic composites caused by thermal expansion mismatch. Acta Metall Mater 39(8):1883–1890

    Article  Google Scholar 

  41. Tang SB, Tang CA, Liang ZZ, Zhang YF (2011) Influence of heterogeneity on strength and failure characterization of cement-based composite subjected to uniform thermal loading. Constr Build Mater 25(8):3382–3392

    Article  Google Scholar 

  42. Yan C, Zheng H (2017) A coupled thermo-mechanical model based on the combined finite-discrete element method for simulating thermal cracking of rock. Int J Rock Mech Min Sci 91:170–178

    Article  Google Scholar 

  43. Briche G, Tessier-Doyen N, Huger M, Chotard T (2008) Investigation of the damage behaviour of refractory model materials at high temperature by combined pulse echography and acoustic emission techniques. J Eur Ceram Soc 28(15):2835–2843

    Article  Google Scholar 

  44. Lubachevsky BD, Stillinger FH (1990) Geometric properties of random disk packings. J Stat Phys 60(5):561–583

    Article  MathSciNet  MATH  Google Scholar 

  45. Donev A, Cisse I, Sachs D, Variano EA, Stillinger FH, Connelly R, Torquato S, Chaikin PM (2004) Improving the density of jammed disordered packings using ellipsoids. Science 303(5660):990–3

    Article  Google Scholar 

  46. Przemieniecki JS (1968) Theory of matrix structural analysis. McGraw-Hill, New York

    MATH  Google Scholar 

  47. Fakhimi A, Villegas T (2006) Application of dimensional analysis in calibration of a discrete element model for rock deformation and fracture. Rock Mech Rock Eng 40(2):193

    Article  Google Scholar 

  48. Kumar R, Rommel S, Jauffrès D, Lhuissier P, Martin CL (2016) Effect of packing characteristics on the discrete element simulation of elasticity and buckling. Int J Mech Sci 110:14–21

    Article  Google Scholar 

  49. Liao C, Chang T-P, Young D-H, Chang C (1997) Stress–strain relationship for granular materials bases on hypothesis of best fit. Int J Solids Struct 34:4087–4100

    Article  MATH  Google Scholar 

  50. Hashin Z, Shtrikman S (1963) A variational approach to the theory of the elastic behaviour of multiphase materials. J Mech Phys Solids 11(2):127–140

    Article  MathSciNet  MATH  Google Scholar 

  51. Levin VM (1967) On the coefficients of thermal expansion of heterogeneous materials. Mekhanika Tverdogo Tela 2:58–61

    Google Scholar 

  52. Zhou M (2003) A new look at the atomic level virial stress: on continuum-molecular system equivalence. Proc R Soc Lond A Math Phys Eng Sci 459(2037):2347–2392

    Article  MATH  Google Scholar 

  53. Hahn M, Schwarz M, Kröplin B-H, Wallmersperger T (2011) Discrete element method for the thermal field: proof of concept and determination of the material parameters. Comput Mater Sci 50(10):2771–2784

    Article  Google Scholar 

  54. Moukadiri D, Leclerc W, Kamel K, Aboura Z, Guessasma M, Bellenger E, Druesne F (2019) Halo approach to evaluate the stress distribution in 3D discrete element method simulation: validation and application to flax/bio based epoxy composite. Model Simul Mater Sci Eng 27(6):065005

    Article  Google Scholar 

Download references

Acknowledgements

The authors would like to thank the European Union for its financial support of CUBISM project under the INTERREG V France-Wallonie-Vlaanderen Program FWV \(\hbox {N}^\circ \) 1.1.22.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to G. Alhajj Hassan.

Ethics declarations

Conflict of interest

The authors declare that they have 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

Alhajj Hassan, G., Leclerc, W., Pélegris, C. et al. On the suitability of a 3D discrete element method to model the composite damage induced by thermal expansion mismatch. Comp. Part. Mech. 7, 679–698 (2020). https://doi.org/10.1007/s40571-019-00298-1

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40571-019-00298-1

Keywords

Navigation