Simulations of instability in dynamic fracture by the cracking particles method

Engineering Fracture Mechanics

Volumn 76, Issue 6, 2009, Pages 730-741

  Rabczuk, Timon ^a   Song, Jeong Hoon ^b   Belytschko, Ted ^b  

^a UNIVERSITY OF CANTERBURY   (New Zealand)

^b Northwestern University   (United States)

Author keywords

Dynamic instability; Meshfree cracking particle method; Microcrack branching; Microvoids

Indexed keywords

CRACKS; ENERGY DISSIPATION; FLUID DYNAMICS;

BRITTLE MATERIALS; CRACK INSTABILITIES; CRACK SPEED; DYNAMIC FRACTURES; DYNAMIC INSTABILITY; EXPERIMENTAL OBSERVATIONS; MESHFREE CRACKING PARTICLE METHOD; MICRO-DEFECTS; MICROCRACK BRANCHING; MICROSTRUCTURAL DEFECTS; MICROVOIDS; RAYLEIGH WAVE SPEED; SALIENT FEATURES;

SPEED;

EID: 62649132841     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.engfracmech.2008.06.002     Document Type: Article

References (41)

1. Ravi-Chandar K., and Knauss W.G. An experimental investigation into dynamic fracture: II. Microstructural aspects. Int J Fract 26 (1984) 65-80
2. Ravi-Chandar K., and Knauss W.G. An experimental investigation into dynamic fracture: III. On steady-state crack propagation and crack branching. Int J Fract 26 (1984) 141-154
3. Sharon E., Gross S.P., and Fineberg J. Energy dissipation in dynamic fracture. Phys Rev Lett 76 12 (1996) 2117-2120
4. Sharon E., and Fineberg J. Confirming the continuum theory of dynamic brittle fracture for fast cracks. Lett Nat 397 (1999) 333-335
5. Ravi-Chandar K. Dynamic fracture (2004), Elsevier, Boston
6. Rabczuk T., and Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int J Numer Meth Engng 61 (2004) 2316-2343
7. Grégoire D., Maigre H., Réthoré J., and Combescure A. Dynamic crack propagation under mixed-mode loading - comparison between experiments and X-FEM simulations. Int J Solids Struct 44 (2007) 6517-6534
8. Zhou F., Molinari J.F., and Shioya T. A rate-dependent cohesive model for simulating dynamic crack propagation in brittle materials. Engng Fract Mech 72 (2005) 1383-1410
9. Xu X.-P., and Needleman A. Numerical simulation of fast crack growth in brittle solids. J Mech Phys Solids 42 9 (1994) 1397-1434
10. Camacho G., and Ortiz M. Computational modelling of impact damage in brittle materials. Int J Solids Struct 33 (1996) 2899-2938
11. Belytschko T., and Black T. Elastic crack growth in finite elements with minimal remeshing. Int J Numer Meth Engng 45 5 (1999) 601-620
12. Moës N., Dolbow J., and Belytschko T. A finite element method for crack growth without remeshing. Int J Numer Meth Engng 46 1 (1999) 131-150
13. Stolarska M., Chopp D.L., Moës N., and Belytschko T. Modeling crack growth by level sets in the extended finite element method. Int J Numer Meth Engng 51 8 (2001) 943-960
14. Belytschko T., Moës N., Usui S., and Parimi C. Arbitrary discontinuities in finite elements. Int J Numer Meth Engng 50 4 (2001) 993-1013
15. Fries T.P., and Belytschko T. The intrinsic XFEM: a method for arbitrary discontinuities without additional unknowns. Int J Numer Meth Engng 68 (2006) 1358-1385
16. Menouillard T., Réthoré J., Combescure A., and Bung H. Efficient explicit time stepping for the eXtended Finite Element Method. Int J Numer Meth Engng 68 (2006) 911-939
17. Song J.H., Areias P.M.A., and Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. Int J Numer Meth Engng 67 (2006) 868-893
18. Xiao Q.Z., Karihaloo B.L., and Liu X.Y. Incremental-secant modulus iteration scheme and stress recovery for simulating cracking process in quasi-brittle materials using XFEM. Int J Numer Meth Engng 69 (2007) 2606-2635
19. Asadpoure A., and Mohammadi S. Developing new enrichment functions for crack simulation in orthotropic media by the extended finite element method. Int J Numer Meth Engng 69 (2007) 2150-2172
20. Prabel B., Combescure A., Gravouil A., and Marie S. Level set X-FEM non-matching meshes: application to dynamic crack propagation in elastic-plastic media. Int J Numer Meth Engng 69 (2007) 1553-1569
21. Rabczuk T., Areias P.M.A., and Belytschko T. A simplified meshfree method for shear bands with cohesive surfaces. Int J Numer Meth Engng 69 (2007) 993-1021
22. Bordas S., and Moran B. Enriched finite elements and level sets for damage tolerance assessment of complex structures. Engng Fract Mech 73 (2006) 1176-1201
23. Bordas S., Nguyen V.P., Dunant C., Nguyen-Dang H., and Guidoum A. An extended finite element library. Int J Numer Meth Engng 71 (2007) 703-732
24. Song JH, Wang HW, Belytschko T. A comparative study on finite element methods for dynamic fracture. Comput Mech. doi: 10.1007/s00466-007-0210-x.
25. Zhang Z., Paulino G.H., and Celes W. Extrinsic cohesive modelling of dynamic fracture and microbranching instability in brittle materials. Int J Numer Meth Engng 72 (2007) 893-923
26. Swegle JW, Attaway SW, Heinstein MW, Mello FJ, Hicks DL. An analysis of smoothed particle hydrodynamics, vol SAND-93-2513. Albuquerque (NM): Sandia National Laboratories; 1994.
27. Swegle J.W., Hicks D.L., and Attaway S.W. Smoothed particle hydrodynamics stability analysis. J Comput Phys 116 (1995) 123-134
28. Rabczuk T., Belytschko T., and Xiao S.P. Stable particle methods based on lagrangian kernels. Comp Meth Appl Mech Engng 193 (2004) 1035-1063
29. Belytschko T., Lu Y.Y., and Gu L. Element-free Galerkin methods. Int J Numer Meth Engng 37 (1994) 229-256
30. Belytschko T., Krongauz Y., Organ D., Fleming M., and Krysl P. Meshless methods: an overview and recent developments. Comp Meth Appl Mech Engng 139 (1996) 3-47
31. Belytschko T., Lu Y.Y., GU L., and Tabbara M. Element-free Galerkin methods for static and dynamic fracture. Int J Numer Meth Engng 32 (1995) 2547-2570
32. Lu Y.Y., Belytschko T., and Tabbara M. Element-free Galerkin method for wave propagation and dynamic fracture. Comp Meth Appl Mech Engng 126 (1995) 131-153
33. Krysl P., and Belytschko T. The element free Galerkin method for dynamic propagation of arbitrary 3-D cracks. Int J Numer Meth Engng 44 (1999) 767-800
34. Sharon E., Gross S.P., and Fineberg J. Local crack branching as a mechanism for instability in dynamic fracture. Phys Rev Lett 74 25 (1995) 5096-5099
35. Belytschko T., Liu W.K., and Moran B. Nonlinear finite elements for continua and structures (2000), John Wiley & Sons Ltd., New York
36. Papoulia K.D., Sam C.H., and Vavasis S.A. Time continuity in cohesive finite element modeling. Int J Numer Meth Engng 58 (2003) 679-701
37. Fineberg J., Gross S.P., Marder M., and Swinney H.L. Instability in dynamic fracture. Phys Rev Lett 67 (1991) 457-460
38. Fineberg J., Gross S.P., Marder M., and Swinney H.L. Instability in the propagation of fast cracks. Phys Rev B 45 (1992) 5146-5154
39. Sharon E., and Fineberg J. Microbranching instability and the dynamic fracture of brittle materials. Phys Rev B 54 10 (1996) 7128-7139
40. Fineberg J., and Marder M. Instability in dynamic fracture. Phys Rep 313 (1999) 1-108
41. Needleman A., and Rosakis A.J. The effect of bond strength and loading rate on the conditions governing the attainment of intersonic crack growth along interfaces. J Mech Phys Solids 47 (1999) 2411-2449