Asymptotic fields at frictionless and frictional cohesive crack tips in quasibrittle materials

Journal of Mechanics of Materials and Structures

Volumn 1, Issue 5, 2006, Pages 881-910

  Xiao, Qizhi ^a   Karihaloo, Bhushan Lal ^a  

^a CARDIFF UNIVERSITY   (United Kingdom)

Author keywords

Asymptotic field; Cohesion separation laws; Cohesive crack tip; Coulomb friction; Quasibrittle material

Indexed keywords

CRACK PROPAGATION; FRICTION; POLYNOMIALS; SEPARATION;

ASYMPTOTIC FIELD; COHESIVE CRACK MODELS; COHESIVE CRACKS; COULOMB FRICTIONS; ENRICHMENT FUNCTIONS; QUASIBRITTLE MATERIAL; SEPARATION LAWS; SPECIAL POLYNOMIALS;

CRACK TIPS;

EID: 33947286819     PISSN: 15593959     EISSN: None     Source Type: Journal    
DOI: 10.2140/jomms.2006.1.881     Document Type: Article

References (46)

1. H. M. Abdalla and B. L. Karihaloo, "A method for constructing the bilinear tension softening diagram of concrete corresponding to its true fracture energy", Mag. Concr. Res. 56:10 (2004), 597-604.
2. I. Babuška, U. Banerjee, and J. E. Osborn, "Survey of meshless and generalized finite element methods: A unified approach", Acta Numerica 12 (2003), 1-125.
3. G. I. Barenblatt, "The mathematical theory of equilibrium cracks in brittle fracture", Adv. Appl. Mech. 7 (1962), 55-129.
4. M. Bialas and Z. Mróz, "Modelling of progressive interface failure under combined normal compression and shear stress", Int. J. Solids Struct. 42:15 (2005), 4436-4467.
5. R. de Borst, M. A. Gutierrez, G. N. Wells, J. J. C. Remmers, and H. Askes, "Cohesive-zone models, higher-order continuum theories and reliability methods for computational failure analysis", Int. J. Numer. Methods Eng. 60:1 (2004), 289-315.
6. A. Carpinteri and G. Colombo, "Numerical analysis of catastrophic softening behaviour (snapback instability)", Comput. Struct. 31:4 (1989), 607-636.
7. N. Chandra, H. Li, C. Shet, and H. Ghonem, "Some issues in the application of cohesive zone models for metal-ceramic interfaces", Int. J. Solids Struct. 39:10 (2002), 2827-2855.
8. Y. J. Chao and S. Yang, "Higher order crack tip fields and its implication for fracture of solids under mode II conditions", Eng. Fract. Mech. 55:5 (1996), 777-794.
9. G. Cocchetti, G. Maier, and X. P Shen, "Piecewise linear models for interfaces and mixed mode cohesive cracks", Comput. Model. Eng. Sci. 3:3 (2002), 279-298.
10. H. A. W. Cornelissen, D. A. Hordijk, and H. W. Reinhardt, "Experimental determination of crack softening characteristics of normalweight and lightweight concrete", Heron 31:2 (1986), 45-56.
11. X. M. Deng, "An asymptotic analysis of stationary and moving cracks with frictional contact along bimaterial interfaces and in homogeneous solids", Int. J. Solids Struct. 31:17 (1994), 2407-2429.
12. D. S. Dugdale, "Yielding of steel sheets containing slits", J. Mech. Phys. Solids 8:2 (1960), 100-104.
13. M. Elices, G. V. Guinea, J. Gómez, and J. Planas, "The cohesive zone model: advantages, limitations and challenges", Eng. Fract. Mech. 69:2 (2002), 137-163.
14. A. Hansbo and P Hansbo, 'A finite element method for the simulation of strong and weak discontinuities in solid mechanics", Comput. Methods Appl. Mech. Eng. 193:33-35 (2004), 3523-3540.
15. A. Hillerborg, M. Modéer, and P. E. Petersson, "Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements", Cem. Concr Res. 6:6 (1976), 773-782.
16. S. S. Hong and K. S. Kim, "Extraction of cohesive-zone laws from elastic far-fields of a cohesive crack tip: a field projection method", J. Mech. Phys. Solids 51:7 (2003), 1267-1286.
17. J. W. Hutchinson and A. G. Evans, "Mechanics of materials: top-down approaches to fracture", Acta Mater. 48:1 (2000), 125-135.
18. B. L. Karihaloo, Fracture mechanics and structural concrete, Addison Wesley Longman, UK, 1995.
19. B. L. Karihaloo, "Size effect in shallow and deep notched quasi-brittle structures", Int. J. Fract. 95:1-4 (1999), 379-390.
20. B. L. Karihaloo and Q. Z. Xiao, "Linear and nonlinear fracture mechanics", pp. 81-212 in Comprehensive structural integrity, II: fundamental theories and mechanisms of failure, vol. 2, edited by B. L. Karihaloo and W. G. Knauss, Elsevier Pergamon, UK, 2003.
21. B. L. Karihaloo and Q. Z. Xiao, "Modelling of stationary and growing cracks in FE framework without remeshing: a state-of-the-art review", Comput. Struct. 81:3 (2003), 119-129.
22. B. L. Karihaloo, H. M. Abdalla, and T. Imjai, "A simple method for determining the true specific fracture energy of concrete", Mag. Concr. Res. 55:5 (2003), 471-481.
23. J. B. Leblond and J. L. Frelat, "Crack kinking from an initially closed, ordinary or interface crack, in the presence of friction", Eng. Fract. Mech. 71:3 (2004), 289-307.
24. X. Y. Liu, Q. Z. Xiao, and B. L. Karihaloo, "XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials", Int. J. Numer. Methods Eng. 59:8 (2004), 1103-1118.
25. N. Moës and T. Belytschko, "Extended finite element method for cohesive crack growth", Eng. Fract. Mech. 69:7 (2002), 813-833.
26. N. Moës, J. Dolbow, and T. Belytschko, "A finite element method for crack growth without remeshing", Int. J. Numer. Methods Eng. 46:1 (1999), 131-150.
27. Z. Mróz and M. Bialas, "A simplified analysis of interface failure under compressive normal stress and monotonic or cyclic shear loading", Int. J. Numer. Anal. Methods Geomech. 29:4 (2005), 337-368.
28. N. I. Muskhelishvili, Some basic problems of mathematical theory of elasticity, Noordhoff, Holland, 1953.
29. D. R. J. Owen and A. J. Fawkes, Engineering fracture mechanics: numerical methods and applications, Pineridge Press Ltd., Swansea, UK, 1983.
30. J. Planas, Z. P. Bazant, and M. Jirasek, "Reinterpretation of Karihaloo's size effect analysis for notched quasibrittle structures", Int. J. Fract. 111:1 (2001), 17-28.
31. J. Planas, M. Elices, G. V. Guinea, F. J. Gómez, D. A. Cendón, and I. Arbilla, "Generalizations and specializations of cohesive crack models", Eng. Fract. Mech. 70:14 (2003), 1759-1776.
32. J. J. C. Remmers, R. de Borst, and A. Needleman, "A cohesive segments method for the simulation of crack growth", Comput. Mech. 31:1-2 (2003), 69-77.
33. J. R. Rice, "Elastic fracture mechanics concepts for interfacial cracks", J. Appl. Mech. (Trans. ASME) 55 (1988), 98-103.
34. G. C. Sih and H. Liebowitz, Mathematical theories of brittle fracture, vol. II, Chapter Fracture: an advanced treatise, pp. 67-190, Academic Press, New York, 1968.
35. A. N. Stroh, "Dislocations and cracks in anisotropic elasticity", Philos. Mag. (8) 3 (1958), 625-646.
36. T. Strouboulis, K. Copps, and I. Babuška, "The generalized finite element method", Comput. Methods Appl. Mech. Eng. 190:32-33 (2001), 4081-4193.
37. Z. Suo, "Singularities, interfaces and cracks in dissimilar anisotropic media", Proc. Roy. Soc. London Ser. A 427:1873 (1990), 331-358.
38. S. Valente, "Influence of friction on cohesive crack-propagation", pp. 695-704 in Fracture processes in concrete, rock and ceramics, edited by J. G. M. van Mier et al., RILEM Proceedings 13, London, 1991.
39. M. Wecharatana, "Brittleness index of cementitious composite", in Serviceability and durability ofconstruction materials, edited by B. A. Suprenant, ASCE Publications, New York, 1990.
40. G. N. Wells and L. J. Sluys, "A new method for modeling cohesive cracks using finite elements", Int. J. Numer. Methods Eng. 50:12 (2001), 2667-2682.
41. M. L. Williams, "On the stress distribution at the base of a stationary crack", J. Appl. Mech. (Trans. ASME) 24 (1957), 109-114.
42. L. Xia, T. C. Wang, and C. F. Shih, "Higher-order analysis of crack tip fields in elastic power-law hardening materials", J. Mech. Phys. Solids 41:4 (1993), 665-687.
43. Q. Z. Xiao and B. L. Karihaloo, "Recent developments of the extended/generalized FEM and a comparison with the FEM", pp. 303-324 in Developments and applications of solid mechanics, Proceedings of the Symposium for Professor M. G. Huang's 90th Birthday, edited by X. P Wu, Press of University of Science and Technology of China, China, 2005.
44. Q. Z. Xiao, B. L. Karihaloo, and X. Y. Liu, "Incremental-secant modulus iteration scheme and stress recovery for simulating cracking process in quasi-brittle materials using XFEM", Int. J. Numer. Mech. Eng. (2006, in press).
45. S. Yang, Y. J. Chao, and M. A. Sutton, "Higher order asymptotic crack tip fields in a power-law hardening material", Eng. Fract. Mech. 45:1 (1993), 1-20.
46. S. Yang, F. G. Yuan, and X. Cai, "Higher order asymptotic elastic-plastic crack-tip fields under antiplane shear", Eng. Fract. Mech. 54:3 (1996), 405-422.