Advertisement

International Journal of Fracture

, Volume 170, Issue 1, pp 49–66 | Cite as

Simulation of dynamic fracture with the Material Point Method using a mixed J-integral and cohesive law approach

  • Scott G. Bardenhagen
  • John A. Nairn
  • Hongbing Lu
Original Paper

Abstract

A new approach to simulating fracture, in which toughness is partitioned between the crack tip and, optionally, a process zone, is applied to dynamic fracture processes. In this approach, classical fracture mechanics determines crack tip propagation, and cohesive laws characterize process zone response and determine crack root and process zone propagation. The approach is implemented in the Material Point Method, a particle method in which the fracture path is unconstrained by a body-fitted mesh. The approach is found suitable for modeling a range of dynamic fracture processes, from brittle fracture to fracture with crack bridging. A variety of ways of partitioning toughness are explored with the aim of distinguishing model parameters via experimental measurements, particularly R curves. While no unique relationship exists, R curves, or effective R curves, on a suite of materials would provide substantial insight into model parameters. Advantages to the approach are identified, both in versatility and in regards to practical matters associated with implementing numerical fracture algorithms. It is found to perform well in dynamic fracture scenarios.

Keywords

Dynamic fracture J-integral Cohesive elements MPM 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abu Al-Rub RK, Kim S-M (2010) Computational applications of a coupled plasticity-damage constitutive model for simulating plain concrete fracture. Eng Fract Mech 77: 1577–1603CrossRefGoogle Scholar
  2. Arias I, Knap J, Chalivendra V, Hong S, Ortiz M, Rosakis A (2007) Numerical modelling and experimental validation of dynamic fracture events along weak planes. Comput Methods Appl Mech Eng 196(37–40): 3833–3840CrossRefGoogle Scholar
  3. Atluri S, Zhu T (2000) New concepts in meshless methods. Int J Numer Methods Eng 47(1–3): 537–556CrossRefGoogle Scholar
  4. Babuska I, Melenk J (1997) The partition of unity method. Int J Numer Methods Eng 40(4): 727–758CrossRefGoogle Scholar
  5. Bardenhagen S, Kober E (2004) The generalized interpolation Material Point Method. Comput Model Eng Sci 5(6): 477–496Google Scholar
  6. Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P (1996) Meshless methods: an overview and recent developments. Comput Methods Appl Mech Eng 139(1–4): 3–47CrossRefGoogle Scholar
  7. Bentur A, Mindess S (2006) Fibre reinforced cementitious composites Spons Architecture Price BookGoogle Scholar
  8. Blackman B, Hadavinia H, Kinloch A, Williams J (2003) The use of a cohesive zone model to study the fracture of fibre composites and adhesively-bonded joints. Int J Fract 119(1): 25–46CrossRefGoogle Scholar
  9. Borst R, Remmers J, Needleman A (2006) Mesh-independent discrete numerical representations of cohesive-zone models. Eng Fract Mech 73(2): 160–177CrossRefGoogle Scholar
  10. Brackbill J, Kothe D, Ruppel H (1988) FLIP: a low-dissipation, particle-in-cell method for fluid flow. Comput Phys Commun 48(1): 25–38CrossRefGoogle Scholar
  11. Burgess D, Sulsky D, Brackbill J (1992) Mass matrix formulation of the FLIP particle-in-cell method. J Comput Phys 103(1): 1–15CrossRefGoogle Scholar
  12. Chen L, Zhang YY (2010) Dynamic fracture analysis using discrete cohesive crack method. Int J Numer Method Biomed Eng 26(11): 1493–1502. doi: 10.1002/cnm.1232 CrossRefGoogle Scholar
  13. Damjanac B, Detournay E (1995) Numerical modeling of normal wedge indentation in rocks. In: 35th US Symposium on Rock Mechanics. AA Balkema, Rotterdam, Netherlands, pp 349–354Google Scholar
  14. Daphalapurkar N, Lu H, Coker D, Komanduri R (2007) Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method. Int J Fract 143(1): 79–102CrossRefGoogle Scholar
  15. Demkowicz L, Oden J (1986) An adaptive characteristic Petrov-Galerkin finite element method for convection-dominated linear and nonlinear parabolic problems in one space variable. J Comput Phys 67(1): 188–213CrossRefGoogle Scholar
  16. Dugdale D (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8(2): 100–104CrossRefGoogle Scholar
  17. Graham-Brady L (2010) Statistical characterization of meso-scale uniaxial compressive strength in brittle materials with randomly occurring flaws. Int J Solids Struct 47: 2398–2413CrossRefGoogle Scholar
  18. Guo Y, Nairn J (2004) Calculation of J-integral and stress intensity factors using the Material Point Method. Comput Model Eng Sci 6: 295–308Google Scholar
  19. Guo Y, Nairn J (2006) Three-dimensional dynamic fracture analysis using the Material Point Method. Comput Model Eng Sci 16(3): 141Google Scholar
  20. Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fract 162(1–2): 229–244CrossRefGoogle Scholar
  21. Harlow F (1964) The particle-in-cell computing method for fluid dynamics. Methods Comput Phys 3: 319–343Google Scholar
  22. Huang H, Detournay E, Bellier B (1999) Discrete element modelling of rock cuttingGoogle Scholar
  23. Johnson C (1987) Numerical solution of partial differential equations by the finite element method. Cambridge University Press, CambridgeGoogle Scholar
  24. Khoei A, Moslemi H, Majd Ardakany K, Barani O, Azadi H (2009) Modeling of cohesive crack growth using an adaptive mesh refinement via the modified-SPR technique. Int J Fract 159(1): 21–41CrossRefGoogle Scholar
  25. Li L, Liu S, Wang H (2011) A meshless method for ductile fracture. Int J Numer Method Biomed Eng 27(2): 251–261CrossRefGoogle Scholar
  26. Li S, Liu WK (2002) Meshfree and particle methods and their applications. Appl Mech Rev 55(1): 1–34CrossRefGoogle Scholar
  27. Liu C, Stout M, Asay B (2000) Stress bridging in a heterogeneous material. Eng Fract Mech 67(1): 1–20CrossRefGoogle Scholar
  28. Matsumoto N, Nairn J (2009) The fracture toughness of medium density fiberboard (MDF) including the effects of fiber bridging and crack-plane interference. Eng Fract Mech 76(18): 2748–2757CrossRefGoogle Scholar
  29. Matsumoto N, Nairn J (2010) Fracture toughness of wood and wood composites during crack propagation. Wood Fiber sci (submitted)Google Scholar
  30. Nairn J (2009) Analytical and numerical modeling of R curves for cracks with bridging zones. Int J Fract 155(2): 167–181CrossRefGoogle Scholar
  31. Needleman A (1999) An analysis of intersonic crack growth under shear loading. J Appl Mech 66: 847CrossRefGoogle Scholar
  32. Nishioka T (1997) Computational dynamic fracture mechanics. Int J Fract 86(1): 127–159CrossRefGoogle Scholar
  33. Nishioka T, Atluri S (1983) Path-independent integrals, energy release rates, and general solutions of near-tip fields in mixed-mode dynamic fracture mechanics. Eng Fract Mech 18(1): 1–22CrossRefGoogle Scholar
  34. Nistor I, PantalÈ O, Caperaa S (2008) Numerical implementation of the eXtended Finite Element Method for dynamic crack analysis. Adv Eng softw 39(7): 573–587CrossRefGoogle Scholar
  35. Pandolfi A, Ortiz M (2002) An efficient adaptive procedure for three-dimensional fragmentation simulations. Eng Comput 18(2): 148–159CrossRefGoogle Scholar
  36. Rosakis A, Samudrala O, Coker D (1999) Cracks faster than the shear wave speed. Science 284(5418): 1337CrossRefGoogle Scholar
  37. Silling SA (2000) Reformulation of elasticity theory for discontinuities and long-range forces. J Mech Phys Solids 48(1): 175–209. doi: 10.1016/s0022-5096(99)00029-0 CrossRefGoogle Scholar
  38. Sulsky D, Chen Z, Schreyer H (1994) A particle method for history-dependent materials. Comput Methods Appl Mech Eng 118(1–2): 179–196CrossRefGoogle Scholar
  39. Sulsky D, Zhou S, Schreyer H (1995) Application of a particle-in-cell method to solid mechanics. Comput Phys Commun 87(1–2): 236–252CrossRefGoogle Scholar
  40. Xu X, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 42(9): 1397–1434CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Scott G. Bardenhagen
    • 1
  • John A. Nairn
    • 2
  • Hongbing Lu
    • 3
  1. 1.Wasatch Molecular IncorporatedSalt Lake CityUSA
  2. 2.Oregon State UniversityCorvallisUSA
  3. 3.The University of Texas at DallasRichardsonUSA

Personalised recommendations