An overview of a hybrid crack element and determination of its complete displacement field

Engineering Fracture Mechanics

Volumn 74, Issue 7, 2007, Pages 1107-1117

  Xiao, Q Z ^a,b   Karihaloo, B L ^b  

^a SHANGHAI JIAO TONG UNIVERSITY   (China)

^b CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Boundary collocation method (BCM); Complete displacement field; Displacement discontinuity; Hybrid crack element (HCE); Least squares

Indexed keywords

FINITE ELEMENT METHOD; FRACTURE MECHANICS; LEAST SQUARES APPROXIMATIONS; STRESS INTENSITY FACTORS;

BOUNDARY COLLOCATION METHOD; DISPLACEMENT DISCONTINUITY; HYBRID CRACK ELEMENT;

CRACKS;

CRACKS; FINITE ELEMENT METHOD; FRACTURE MECHANICS; LEAST SQUARES APPROXIMATIONS; STRESS INTENSITY FACTORS;

EID: 33847240931     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.engfracmech.2006.12.022     Document Type: Article

References (54)

1. Williams M.L. On the stress distribution at the base of a stationary crack. ASME J Appl Mech 24 (1957) 109-114
2. Owen D.R.J., and Fawkes A.J. Engineering fracture mechanics: numerical methods and applications (1983), Pineridge Press, Swansea, UK
3. Karihaloo B.L., and Xiao Q.Z. Accurate determination of the coefficients of elastic crack tip asymptotic field by a hybrid crack element with p-adaptivity. Engng Fract Mech 68 (2001) 1609-1630
4. Karihaloo B.L., and Xiao Q.Z. Linear and nonlinear fracture mechanics. In: Milne I., Ritchie R.O., and Karihaloo B.L. (Eds). Comprehensive structural integrity. In: Karihaloo B.L., and Knauss W.G. (Eds). Fundamental theories and mechanisms of failure Volume 2 (2003), Elsevier Pergamon, UK 81-212 [Chapter 2.03]
5. Larsson S.G., and Carlsson A.J. Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic-plastic materials. J Mech Phys Solids 21 (1973) 263-277
6. Rice J.R. Limitations to the small scale yielding approximation for crack tip plasticity. J Mech Phys Solids 22 (1974) 17-26
7. Du Z.Z., and Hancock J.W. The effect of non-singular stresses on crack tip constraint. J Mech Phys Solids 39 (1991) 555-567
8. Chao YJ, Zhang X. Constraint effect in brittle fracture. In: Piascik R, editor. ASTM STP 1296, Fatig Fract Mech, 1997;27:41-60.
9. Dyskin A.V. Crack growth criteria incorporating non-singular stresses: size effect in apparent fracture toughness. Int J Fract 83 (1997) 191-206
10. Karihaloo B.L., Abdalla H.M., and Xiao Q.Z. Size effect in concrete beams. Engng Fract Mech 70 (2003) 979-993
11. Liebowitz H., and Moyer E.T. Finite element methods in fracture mechanics. Comput Struct 31 (1989) 1-9
12. Ingraffea A.R., and Wawrzynek P.A. Finite element methods for linear elastic fracture mechanics. In: Milne I., Ritchie R.O., and Karihaloo B.L. (Eds). Comprehensive structural integrity. In: de Borst R., and Mang H.A. (Eds). Numerical and computational methods Volume 3 (2003), Elsevier Pergamon, UK 1-88 [Chapter 3.01]
13. Aliabadi M.H. Boundary element methods in linear elastic fracture mechanics. In: Milne I., Ritchie R.O., and Karihaloo B.L. (Eds). Comprehensive structural integrity. In: de Borst R., and Mang H.A. (Eds). Numerical and computational methods Volume 3 (2003), Elsevier Pergamon, UK 89-125 [Chapter 3.02]
14. Karihaloo B.L., and Xiao Q.Z. Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Comput Struct 81 (2003) 119-129
15. Tong P., Pian T.H.H., and Lasry S.J. A hybrid element approach to crack problems in plane elasticity. Int J Numer Meth Engng 7 (1973) 297-308
16. Lin KY, Tong P, Orringer O. Effect of shape and size on hybrid crack-containing finite elements. Proceedings of the 2nd American Society of mechanical engineers pressure vessels and piping conference. San Francisco, California, June 1975.
17. Orringer O., Lin K.Y., Stalk G., Tong P., and Mar J.W. K-solutions with assumed-stress hybrid elements. ASCE J Struct Div 103 (1977) 321-334
18. Tong P. A hybrid crack element for rectilinear anisotropic material. Int J Numer Meth Engng 11 (1977) 377-382
19. Lin KY, Tong P. A hybrid crack element for the fracture mechanics analysis of composite materials. In: Luxmoore AR, Owen DRJ, editors. Proceedings of the first international conference on numerical methods in fracture mechanics. Swansea, 9-13 January, 1978. p. 733-46.
20. Khalil S.A., Sun C.T., and Hwang W.C. Application of a hybrid finite element method to determine stress intensity factors in unidirectional composites. Int J Fract 31 (1986) 37-51
21. Lin K.Y., and Mar J.W. Finite element analysis of stress intensity factors for cracks at a bimaterial interface. Int J Fract 12 (1976) 521-531
22. Lee J., and Gao H.J. A hybrid finite element analysis of interface cracks. Int J Numer Meth Engng 38 (1995) 2465-2482
23. Lin K.Y., and Tong P. Singular finite-elements for the fracture-analysis of V-notched plate. Int J Numer Meth Engng 15 (1980) 1343-1354
24. Chen M.C., and Sze K.Y. A novel hybrid finite element analysis of bimaterial wedge problems. Engng Fract Mech 68 (2001) 1463-1476
25. Chen M.C., Sze K.Y., and Wang H.T. Analysis of singular stresses in bonded bimaterial wedges by computed eigen solutions and hybrid element method. Commun Numer Meth Engng 17 (2001) 495-507
26. Zhou Y., Wang X.W., and Zheng S.J. Analyses of piezoelectric plates with elliptical notches by special finite element. Int J Mech Sci 47 (2005) 1409-1422
27. Piltner R. Special finite elements with holes and internal cracks. Int J Numer Meth Engng 21 (1985) 1471-1485
28. Ghosh S., and Mukhopadhyay S.N. A material based finite element analysis of heterogeneous media involving Dirichlet tessallations. Comput Meth Appl Mech Engng 104 (1993) 211-247
29. Zhang J., and Katsube N. A hybrid finite element method for heterogeneous materials with randomly dispersed rigid inclusions. Int J Numer Meth Engng 38 (1995) 1635-1653
30. Zeng D., Katsube N., Zhang J.M., and Soboyejo W. Hybrid crack-tip element and its applications. Finite Elem Anal Des 38 (2002) 319-335
31. Wang X.W., Zhou Y., and Zhou W.L. A novel hybrid finite element with a hole analysis of plane piezoelectric medium with defects. Int J Solids Struct 41 (2004) 7111-7128
32. Kuna M. Some applications of the finite element method to fracture mechanics of elastic and elastic-plastic bodies. In: Luxmoore AR, Owen DRJ, editors. Proceedings of the first international conference on numerical methods in fracture mechanics. Swansea, 9-13 January, 1978. p. 537-49.
33. Knesl Z. Evaluation of the elastic T-stress using a hybrid finite element approach. Int J Fract 70 (1995) R9-R14
34. Karihaloo B.L., and Xiao Q.Z. Higher order terms of the crack tip asymptotic field for a notched three-point bend beam. Int J Fract 112 (2001) 111-128
35. Karihaloo B.L., and Xiao Q.Z. Higher order terms of the crack tip asymptotic field for a wedge-splitting specimen. Int J Fract 112 (2001) 129-137
36. Xiao Q.Z., and Karihaloo B.L. Coefficients of the crack tip asymptotic field for a standard compact tension specimen. Int J Fract 118 (2002) 1-15
37. Karihaloo B.L., Abdalla H., and Xiao Q.Z. Coefficients of the crack tip asymptotic field for wedge-splitting specimens. Engng Fract Mech 70 (2003) 2407-2420
38. Xiao Q.Z., and Karihaloo B.L. Direct evaluation of accurate coefficients of the linear elastic crack tip asymptotic field. Fatig Fract Engng Mater Struct 26 (2003) 719-730
39. Xiao Q.Z., Karihaloo B.L., and Liu X.Y. Direct determination of SIF and higher order terms of mixed mode cracks by a hybrid crack element. Int J Fract 125 (2004) 207-225
40. Song C.M. Evaluation of power-logarithmic singularities, T-stresses and higher order terms of in-plane singular stress fields at cracks and multi-material corners. Engng Fract Mech 72 (2005) 1498-1530
41. Chidgzey S.R., and Deeks A.J. Determination of coefficients of crack tip asymptotic fields using the scaled boundary finite element method. Engng Fract Mech 72 (2005) 2019-2036
42. Su R.K.L., and Feng W.J. Accurate determination of mode I and II leading coefficients of the Williams expansion by finite element analysis. Finite Elem Anal Des 41 (2005) 1175-1186
43. Wu C.C., and Bufler H. Multivariable finite elements: consistency and optimization. Sci China (A) 34 (1991) 284-299
44. Bismarck-Nasr M.N., and Fernandes J.L.C. Hybrid singular elements in fracture mechanics. Proc IMechE Part G: J Aerospace Engineering 220 (2006) 29-49
45. Karihaloo BL, Xiao QZ. Implementation of HCE on a general FE mesh for interacting multiple cracks. Proc ECCOMAS 2004. Jyväskylä, Finland, 24-28 July, 2004. CD-ROM.
46. Xiao QZ, Karihaloo BL. Implementation of hybrid crack element on a general finite element mesh and in combination with XFEM. Comput Meth Appl Mech Engng, in press.
47. Duff I.S., and Reid J.K. The multifrontal solution of indefinite sparse symmetric linear systems. ACM Trans Math Softw 9 (1983) 302-325
48. Moës N., Dolbow J., and Belytschko T. A finite element method for crack growth without remeshing. Int J Numer Meth Engng 46 (1999) 131-150
49. Strouboulis T., Copps K., and Babuška I. The generalized finite element method. Comput Meth Appl Mech Engng 190 (2001) 4081-4093
50. Karihaloo B.L., and Xiao Q.Z. Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review. Comput Struct 81 (2003) 119-129
51. Pian T.H.H., and Sumihara K. Rational approach for assumed stress finite elements. Int J Numer Meth Engng 20 (1984) 1685-1695
52. Pian T.H.H., and Wu C.C. A rational approach for choosing stress term of hybrid finite element formulations. Int J Numer Meth Engng 26 (1988) 2331-2343
53. Xiao Q.Z., Karihaloo B.L., and Williams F.W. Application of penalty-equilibrium hybrid stress element method to crack problems. Engng Fract Mech 63 (1999) 1-22
54. Xiao Q.Z., and Karihaloo B.L. FEM for evaluation of weight functions for SIF, COD and higher order coefficients with application to a typical wedge splitting specimen. Int J Fract 127 (2004) 201-237