Numerical simulation of multiple 3D fracture propagation using arbitrary meshes

Computer Methods in Applied Mechanics and Engineering

Volumn 200, Issue 9-12, 2011, Pages 953-966

  Paluszny, Adriana ^a   Zimmerman, Robert W ^a  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Arbitrary mesh; Brittle; Crack propagation; FEM; J Integral; Three dimensional

Indexed keywords

ANALYTICAL SOLUTIONS; ARBITRARY MESH; BRITTLE; CRACK GEOMETRIES; DECOMPOSITION METHODS; FEM; FINITE ELEMENT; FRACTURE PROPAGATION; GEOMETRIC CONDITIONS; INTEGRATION POINTS; ITERATIVE ALGORITHM; J INTEGRAL; LINEAR ELASTIC; MESH REFINEMENT; NUMERICAL SIMULATION; PIECE-WISE; PROPAGATION CRITERION; SIZE EFFECTS; TETRAHEDRAL MESHES; THICK SLAB; THREE DIMENSIONS;

ALGORITHMS; COMPUTATIONAL EFFICIENCY; COMPUTATIONAL GEOMETRY; CRACK PROPAGATION; CRACKS; CYLINDERS (SHAPES); FINITE ELEMENT METHOD; FRACTURE; STRESS INTENSITY FACTORS; THREE DIMENSIONAL;

THREE DIMENSIONAL COMPUTER GRAPHICS;

EID: 78650627938     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2010.11.013     Document Type: Article

References (66)

1. de Borst R., Remmers J.J.C., Needleman A., Abellan M.-A. Discrete vs smeared crack models for concrete fracture: bridging the gap. Int. J. Numer. Anal. Methods Geomech. 2004, 28:583-607.
2. Jirásek M. Nonlocal models for damage and fracture: comparison of approaches. Int. J. Solids Struct. 1998, 35:4133-4145.
3. Bordas S., Nguyen V., Dunant C., Nguyen-Dang H., Guidoum A. An extended finite element library. Int. J. Numer. Methods Engrg. 2007, 71:703-732.
4. Wyart E., Coulon D., Pardoen T., Remacle J., Lani F. Application of the substructured finite element/extended finite element method to the analysis of cracks in aircraft thin walled structures. Engrg. Fract. Mech. 2009, 76(1):44-58.
5. Rabczuk T., Belytschko T. A three-dimensional large deformation meshfree method for arbitrarily evolving cracks. Comput. Methods Appl. Mech. Engrg. 2007, 196:2777-2799.
6. Bordas S., Rabczuk T., Zi G. Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment. Engrg. Fract. Mech. 2008, 75(5):943-960.
7. Rabczuk T., Belytschko T. Cracking particles: a simplified meshfree method for arbitrarily evolving cracks. Int. J. Numer. Methods Engng. 2004, 61:2316-2343.
8. Carter B.J., Wawrzynek P.A., Ingraffea A.R. Automated 3-D crack growth simulation. Int. J. Numer. Methods Engrg. 2000, 47:229-253.
9. FRANC3D: Concepts/Users Guide. FRANC3D Version 2, 1998. Cornell University, New York. Available from: http://www.cfg.cornell.edu.
10. Lin X.B., Smith R.A. Finite element modelling of fatigue crack growth of surface cracked plates. Part I: The numerical technique. Engrg. Fract. Mech. 1999, 63:503-522.
11. Schöllmann M., Fulland M., Richard H.A. Development of a new software for adaptive crack growth simulations in 3D structures. Engrg. Fract. Mech. 2003, 70:249-268.
12. H.M. Nick, A. Paluszny, S.K. Matthai, M. Blunt, Influence of fracture aperture on solute transport in porous media, Geo Halifax, Halifax, Nova Scotia, Canada, September 20-24, 2009.
13. Paluszny A., Matthai S.K. Impact of fracture development on the effective permeability of porous rocks as determined by 2D discrete fracture growth modeling. J. Geophys. Res. - Solid Earth 2010, 115.
14. Riddell W.T., Ingraffea A.R., Wawrzynek P.A. Experimental observations and numerical predictions of three-dimensional fatigue crack propagation. Engrg. Fract. Mech. 1997, 58(4):293-310.
15. C. Timbrell, P.W. Claydon, G. Cook, Application of ABAQUS to analysis of 3d cracks and fatigue crack growth prediction, in: ABAQUS Users Conference Proceedings. Newport, RI, 1-3 June, 1994, pp. 527-541.
16. G. Dhondt, Automatic three-dimensional cyclic crack propagation predictions with finite elements at the design stage of an aircraft engine, in: Applied Vehicle Technology Panel Symposium on Design Principles and Methods for Aircraft Turbine Engines (NATO-RTO). France: Toulouse, 1998, pp. 331-338.
17. Bremberg D., Dhondt G. Automatic 3-D crack propagation calculations: a pure hexahedral element approach versus a combined element approach. Int. J. Fract. 2009, 157:109-118.
18. Gürses E., Miehe C. A computational framework of three-dimensional configurational-force-driven brittle crack propagation. Comput. Methods Appl. Mech. Engrg. 2009, 198:1413-1428.
19. Cherepanov G.P. The propagation of cracks in a continuous media. J. Appl. Math. Mech. 1967, 31:503-512.
20. Rice J.R. A path independent integral and approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 1968, 379-386.
21. Parks D.M. A stiffness derivative finite element technique for determination of crack tip stress intensity factors. Int. J. Fract. 1974, 10:487-502.
22. Hellen T.K. On the method of virtual crack extensions. Int. J. Numer. Methods Engrg. 1975, 187-207.
23. Huang C.G., Wawrzynek P.A., Ingraffea A.R. On the virtual crack extension method for calculating the derivatives of energy release rates for a 3D planar crack of arbitrary shape under mode I loading. Engrg. Fract. Mech. 2001, 68:925-947.
24. Raju I.S., Newman J.C. Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates. Engrg. Fract. Mech. 1979, 11:817-829.
25. Isida M., Noguchi H. Tension of a plate containing an embedded elliptical crack. Engrg. Fract. Mech. 1984, 20(3):387-408.
26. Chan S.K., Tuba I.S., Wilson W.K. On the finite element method in linear elastic mechanics. Engrg. Fract. Mech. 1970, 2:1-17.
27. Okada H., Kawai H., Araki K. A virtual crack closure-integral method (VCCM) to compute the energy release rates and stress intensity factors based on quadratic tetrahedral finite elements. Engrg. Fract. Mech. 2008, 75:4466-4485.
28. Banks-Sills L. Update: application of the finite element method to linear elastic fracture mechanics. Appl. Mech. Rev. 2010, 63.
29. Pain C.C., Umpleby A.P., de Oliveira C.R.E., Goddard A.J.H. Tetrahedral mesh optimisation and adaptivity for steady-state and transient finite element calculations. Comput. Methods Appl. Mech. Engrg. 2001, 190(29-30):3771-3796.
30. S.J. Owen, A survey of unstructured mesh generation technology, in: Proceedings of 7th international mesh roundtable, Sandia National Laboratories, Dearborn, MI, 1998.
31. B.M. Klingner, J.R. Shewchuk, Aggressive Tetrahedral Mesh Improvement, in: Proceedings of the 16th International Meshing Roundtable, Seattle, Washington, 2007, pp. 3-23.
32. Labelle F., Shewchuk J.R. Isosurface stuffing: fast tetrahedral meshes with good dihedral angles. ACM Trans. Graph. 2007, 26(3):57.1-57.10. August 2007. Special issue on Proceedings of SIGGRAPH 2007.
33. Si H. Constrained Delaunay tetrahedral mesh generation and refinement. Finite Elem. Anal. Design 2010, 46(1-2):33-46.
34. Nikishkov G.P., Atluri S.N. Calculation of fracture mechanics parameters for an arbitrary three-dimensional crack, by the 'equivalent domain integral' method. Int. J. Numer. Methods Engrg. 1987, 24:1801-1821.
35. Cervenka J., Saouma V.E. Numerical evaluation of 3-D SIF for arbitrary finite element meshes. Engrg. Fract. Mech. 1997, 57:541-563.
36. H. Ishikawa, H. Kitagawa, H. Okamura, J-Integral of a mixed mode crack and its application, in: Proceedings of the 3rd International Conference on Mechanical Behaviour of Materials, Pergamon, Oxford, vol. 3, 1979, pp. 447-455.
37. Rigby R.H., Aliabadi M.H. Decomposition of the mixed-mode J-Integral - Revisited. Int. J. Solids Struct. 1998, 35(17):2073-2099.
38. Rajaram H., Socrate S., Parks D.M. Application of domain integral methods using tetrahedral elements to the determination of stress intensity factors. Engrg. Fract. Mech. 2000, 66:455-482.
39. Cottrell J.A., Hughes T.J.R., Bazilevs Y. Isogeometric Analysis: Toward Integration of CAD and FEA 2009, John Wiley & Sons.
40. Paluszny A., Matthai S.K. Numerical modeling of discrete multi-crack growth applied to pattern formation in geological brittle media. Int. J. Solids Struct. 2009, 46:3383-3397.
41. Ingraffea A.R., Wawrzynek P.A. Finite Element Methods for Linear Elastic Fracture Mechanics. Comprehensive Structural Integrity 2003, Elsevier Science Ltd.
42. A. Paluszny, Numerical simulation of fracture pattern development and implications for fluid flow. PhD Thesis. Imperial College London, 2009.
43. Martha L.F., Wawrzynek P.A., Ingraffea A.R. Arbitrary crack representation using solid modeling. Engrg. Comput. 1993, 9:63-68.
44. K.J. Versprille, Computer-Aided Design Applications of the Rational B-Spline Approximation Form. PhD Thesis, Syracuse University, New York, 1975.
45. Cazals F., Pouget M. Smooth surfaces, umbilics, lines of curvatures, foliations, ridges and the medial axis: selected topics. Int. J. Comput. Geometry Appl. 2005, 15(5):511-536.
46. Prautzsch H., Boehm W., Paluszny M. Bezier and B-Spline Techniques 2002, Springer, Berlin.
47. Filip D.J., Ball T.W. Procedurally representing lofted surfaces. IEEE Comput. Graph. Appl. 1989, 2733.
48. Cook R.D., Malkus D.S., Plesha M.E. Concepts and Applications of Finite Element Analysis 1989, John Wiley & Sons. third ed.
49. Jaeger J.C., Cook N.G.W., Zimmerman R.W. Fundamentals of Rock Mechanics 2007, Blackwell Publishing. fourth ed.
50. Banks-Sills L. Application of the finite element method to linear elastic fracture mechanics. Appl. Mech. Rev. 1991, 44:447-461.
51. Field D.A. The legacy of automatic mesh generation from solid modeling. Comput. Aided Geometric Design 1995, 12:651-673.
52. J. Cervenka, Discrete crack modeling in concrete structures. PhD. Thesis, University of Colorado, Boulder, 1994.
53. Zienkiewicz O.C., Zhu J.Z. The superconvergent patch recovery and a posteriori error estimates. Part 1. The recovery technique. Int. J. Numer. Methods Engrg. 1992, 33:1331-1364.
54. H. Rajaram, Three-dimensional fracture mechanics computations using tetrahedral finite elements. PhD Thesis, Massachusetts Institute of Technology, Cambridge, 1997.
55. K.N. Shivakumar, I.S. Raju, An equivalent domain integral for three-dimensional mixed mode fracture problems, NASA CR-182021, 1990.
56. Broek D. Elementary Engineering Fracture Mechanics 1986, Kluwer Academic Publishers.
57. Charles R.J. Static fatigue of glass. J. Appl. Phys. 1958, 29:1549-1560.
58. Erdogan F., Sih O.C. On the crack extension in plates under plane loading and plane shear. J. Basic Engrg. 1963, 85:519-527.
59. Al-Ajmi A.M., Zimmerman R.W. Relation between the Mogi and the Coulomb failure criteria. Int. J. Rock Mech. Mining Sci. 2005, 42:431-439.
60. Weber W., Kuhn G. An optimized predictor-corrector scheme for fast 3D crack growth simulations. Engrg. Fract. Mech. 2008, 75(3-4):452-460.
61. S.K. Matthai, S. Geiger, S.G. Roberts, The complex systems platform CSP3D3.0: User's Guide. Technical report, ETH Zurich Research Reports, 2001.
62. Stüben K. A review of algebraic multigrid. J. Comput. Appl. Math. 2001, 128:281-309.
63. Kishimoto K., Tkeuchi N., Aoki S., Sakata M. Computational accuracy of the J-Integral by the finite element method. Int. J. Pres. Ves. Piping 1990, 44:255-266.
64. P.A. Wawrzynek, B.J. Carter, L. Banks-Sills, The M-Integral for computing stress intensity factors in generally anisotropic materials, NASA Consultant Reports, 2005.
65. Cherepanov G.P. Mechanics of Brittle Fracture 1979, McGraw-Hill, New York.
66. Wicke M., Ritchie D., Klingner B., Burke S., Shewchuk J., O'Brien J. Dynamic local remeshing for elastoplastic simulation. ACM T. Graphic 2010, 29:4.