Cracking node method for dynamic fracture with finite elements

International Journal for Numerical Methods in Engineering

Volumn 77, Issue 3, 2009, Pages 360-385

  Song, Jeong Hoon ^a   Belytschko, Ted ^a  

^a Northwestern University   (United States)

Author keywords

Discrete cohesive crack; Dynamic fracture; Extended finite element method

Indexed keywords

CRACK PROPAGATION; FINITE ELEMENT METHOD; FRACTURE;

ARBITRARY CRACKS; CRACK BRANCHING; CRACK PATHS; CRACK PATTERNS; CRACK SEGMENTS; DISCRETE COHESIVE CRACK; DISCRETE CRACKS; DYNAMIC FRACTURE; EXPLICIT REPRESENTATIONS; EXTENDED FINITE ELEMENT METHOD; FINITE ELEMENTS; FRACTURE BEHAVIORS; FRACTURE PATTERNS; MACROSCOPIC CRACKS;

CRACKS;

EID: 60949096874     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2415     Document Type: Article

References (59)

1. Swenson DV, Ingraffea AR. Modelling mixed-mode dynamic crack propagation using finite elements: theory and applications. Computational Mechanics 1988; 3:187-192.
2. Martha LF, Wawrzynek PA, Ingraffea AR. Arbitrary crack representation using solid modeling. Engineering with Computers 1993; 9:63-82.
3. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45(5):601-620.
4. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46(1):131-150.
5. Babuška I, Melenk JM. The partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40(4):727-758.
6. Stolarska M, Chopp DL, Moës N, Belytschko T. Modeling crack growth by level sets in the extended finite element method. International Journal for Numerical Methods in Engineering 2001; 51(8):943-960.
7. Belytschko T, Moës N, Usui S, Parimi C. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 2001; 50(4):993-1013.
8. Ventura G, Xu JX, Belytschko T. A vector level set method and new discontinuity approximations for crack growth by EFG. International Journal for Numerical Methods in Engineering 2002; 54:923-944.
9. Ventura G, Budyn E, Belytschko T. Vector level sets for description of propagating cracks in finite elements. International Journal for Numerical Methods in Engineering 2003; 58:1571-1592.
10. Prabel B, Combescure A, Gravouil A, Marie S. Level set X-FEM non-matching meshes: application to dynamic crack propagation in elastic-plastic media. International Journal for Numerical Methods in Engineering 2007; 69:1553-1569.
11. Areias PMA, Belytschko T. Analysis of three-dimensional crack initiation and propagation using the extended finite element method. International Journal for Numerical Methods in Engineering 2005; 63:760-788.
12. Belytschko T, Chen H, Xu J, Zi G. Dynamic crack propagation based on loss of hyperbolicity with a new discontinuous enrichment. International Journal for Numerical Methods in Engineering 2003; 58:1873-1905.
13. Zi G, Song JH, Lee SH, Budyn E, Belytschko T. A new method for multiple cracks and its application to fatigue crack growth. Modeling and Simulations in Materials Science and Engineering 2004; 12:901-915.
14. Song JH, Areias PMA, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering 2006; 67:868-893.
15. Areias PMA, Song JH, Belytschko T. A finite-strain quadrilateral shell element based on discrete Kirchhoff-Love constraints. International Journal for Numerical Methods in Engineering 2005; 64:1166-1206.
16. Areias PMA, Song JH, Belytschko T. Analysis of fracture in thin shells by overlapping paired elements. Computer Methods in Applied Mechanics and Engineering 2006; 195:5343-5360.
17. Song JH, Belytschko T. Dynamic fracture of shells subjected to impulsive loads. Journal of Applied Mechanics 2008, in review.
18. Fish J. The s-version of the finite element method. Computers and Structures 1992; 43(3):539-547.
19. Belytschko T, Chiapetta RL, Bartel HD. Efficient large-scale nonlinear transient analysis finite-elements. International Journal for Numerical Methods in Engineering 1976; 10:579-596.
20. Xu X-P, Needleman A. Numerical simulation of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 1994; 42(9):1397-1434.
21. Camacho G, Ortiz M. Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures 1996; 33:2899-2938.
22. Belytschko T, Fish J, Engelmann BE. A finite element with embedded localization zones. Computer Methods in Applied Mechanics and Engineering 1988; 70:59-89.
23. Strouboulis T, Babu.ska I, Coops K. The design and analysis of generalized finite element method. Computer Methods in Applied Mechanics and Engineering 2000; 181:43-69.
24. Duarte CA, Oden JT, Babuška I. Generalized finite element methods for three-dimensional structural mechanics problems. Computers and Structures 2000; 77:215-232.
25. Duarte CA, Reno LG, Simone A. High-order generalized FEM for through-the-thickness branched cracks. International Journal for Numerical Methods in Engineering 2007; 72:325-351.
26. Ortiz M, Pandolfi A. Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. International Journal for Numerical Methods in Engineering 1999; 44:1267-1282.
27. Papoulia KD, Sam CH, Vavasis SA. Time continuity in cohesive finite element modeling. International Journal for Numerical Methods in Engineering 2003; 58:679-701.
28. Papoulia KD, Vavasis SA, Ganguly P. Spatial convergence of crack nucleation using a cohesive finite-element model on a pinwhell-based mesh. International Journal for Numerical Methods in Engineering 2006; 67:1-16.
29. Song JH, Wang HW, Belytschko T. A comparative study on finite element methods for dynamic fracture. Computational Mechanics. DOI: 10.1007/s00466-007-0210-x.
30. Zavattieri PD, Espinosa HD. Grain level analysis of crack initiation and propagation in brittle materials. Acta Materialia 2001; 49:4291-4311.
31. Zhou F, Molinari JF. Dynamic crack propagation with cohesive elements: a methodology to address mesh dependency. International Journal for Numerical Methods in Engineering 2004; 59:1-24.
32. Dvorkin EN, Cuitino AM, Gioia G. Finite elements with displacement interpolated embedded localization lines insensitive to mesh size and distortions. International Journal for Numerical Methods in Engineering 1990; 30:541-564.
33. Simo JC, Oliver J, Armero F. An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids. International Journal for Numerical Methods in Engineering 1993; 12:277-296.
34. Armero F, Garikipati K. An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids. International Journal of Solids and Structures 1996; 33:2863-2885.
35. Jirásek M. Comparative study on finite elements with embedded discontinuities. Computer Methods in Applied Mechanics and Engineering 2000; 188:307-330.
36. Fan R, Fish J. The rs-method for material failure simulations. International Journal for Numerical Methods in Engineering 2008; 73:1607-1623.
37. Remmers JJC, de Borst R, Needleman A. A cohesive segments method for the simulation of crack growth. Computational Mechanics 2003; 31:69-77.
38. de Borst R, Remmers JJC, Needleman A. Mesh-independent discrete numerical representations of cohesive-zone models. Engineering Fracture Mechanics 2006; 73:160-177.
39. Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering 2004; 61:2316-2343.
40. Rabczuk T, Areias PMA, Belytschko T. A simplified meshfree method for shear bands with cohesive surfaces. International Journal for Numerical Methods in Engineering 2007; 69:993-1021.
41. Rabczuk T, Samaniego E. Discontinuous modelling of shear bands using adaptive meshfree methods. Computer Methods in Applied Mechanics and Engineering 2008; 107:641-658.
42. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. Wiley: New York, 2000.
43. Flanagan DP, Belytschko T. A uniform strain hexahedron and quadrilateral with orthogonal hourglass control. International Journal for Numerical Methods in Engineering 1981; 17:679-706.
44. Daniel WJT, Belytschko T. Suppression of spurious intermediate frequency modes in under-integrated elements by combined stiffness/viscous stabilization. International Journal for Numerical Methods in Engineering 2005; 64:335-353.
45. Menouillard T, Réthoré J, Combescure A, Bung H. Efficient explicit time stepping for the extended finite element method. International Journal for Numerical Methods in Engineering 2006; 68:911-939.
46. Menouillard T, Réthoré J, Moës N, Combescure A, Bung H. Mass lumping strategies for X-FEM explicit dynamics: application to crack propagation. International Journal for Numerical Methods in Engineering 2007; DOI: 10.1002/nme.2180.
47. Kalthoff JF, Winkler S. Failure mode transition at high rates of shear loading. International Conference on Impact Loading and Dynamic Behavior of Materials 1987; 1:185-195.
48. Lee YJ, Freund LB. Fracture initiation due to asymmetric impact loading of an edge cracked plate. Journal of Applied Mechanics (ASME) 1990; 57:104-111.
49. Kalthoff JF. Modes of dynamic shear failure in solids. International Journal of Fracture 2000; 101:1-31.
50. Decker RF. Source Book on Maraging Steels. American Society for Metals: Cleveland, OH, 1979.
51. Belytschko T, Tabbara M. Dynamic fracture using element-free Galerkin methods. International Journal for Numerical Methods in Engineering 1996; 39:923-938.
52. Réthoré J, Gravouil A, Combescure A. An energy-conserving scheme for dynamic crack growth using the extended finite element method. International Journal for Numerical Methods in Engineering 2005; 63:631-659.
53. Ramulu M, Kobayashi AS. Mechanics of crack curving and branching - a dynamic fracture analysis. International Journal of Fracture 1985; 27:187-201.
54. Satoh H. On the crack propagation in brittle materials. Ph.D. Thesis, University of Tokyo, Japan, 1996.
55. Ravi-Chandar K. Dynamic fracture of nominally brittle materials. International Journal of Fracture 1998; 90:83-102.
56. Sharon E, Fineberg J. Microbranching instability and the dynamic fracture of brittle materials. Physical Review B 1996; 54(10):7128-7139.
57. Sharon E, Gross SP, Fineberg J. Energy dissipation in dynamic fracture. Physical Review Letters 1996; 76(12):2117-2120.
58. Sharon E, Fineberg J. Confirming the continuum theory of dynamic brittle fracture for fast cracks. Letters to Nature 1999; 397:333-335.
59. Rabczuk T, Song JH, Belytschko T. Simulations of instability in dynamic fracture by the cracking particles method. Engineering Fracture Mechanics 2008, accepted.