Axisymmetric benchmark solutions in fracture mechanics

Engineering Fracture Mechanics

Volumn 102, Issue , 2013, Pages 348-357

  Gordeliy, Elizaveta ^a   Piccinin, Roberto ^a   Napier, John A L ^b   Detournay, Emmanuel ^a,c  

^a University of Minnesota   (United States)

^b UNIVERSITY OF PRETORIA   (South Africa)

^c CSIRO   (Australia)

Author keywords

Axisymmetric crack; Computation; Crack propagation; Stress intensity factors

Indexed keywords

AXISYMMETRIC; AXISYMMETRIC FINITE ELEMENT METHODS; BENCHMARK SOLUTIONS; CRACK PATHS; DISPLACEMENT DISCONTINUITY METHOD; ELASTIC DOMAIN; FULL THREE-DIMENSIONAL;

ASPHALT PAVEMENTS; CALCULATIONS; CRACK PROPAGATION; FINITE ELEMENT METHOD; FRACTURE MECHANICS; STRESS INTENSITY FACTORS;

CRACKS;

EID: 84876339526     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.engfracmech.2013.01.010     Document Type: Article

References (30)

1. Helsing J., Jonsson A. On the accuracy of benchmark tables and graphical results in the applied mechanics literature. J Appl Mech 2002, 69:88-90.
2. Wang J., Mogilevskaya S.G., Crouch S.L. Benchmark results for the problem of interaction between a crack and a circular inclusion. J Appl Mech 2003, 70:619-621.
3. Sneddon I.N. A note on the problem of the penny-shaped crack. Proc Cambust Philos Soc 1965, 61:609-611.
4. Sneddon I.N., Lowengrub M. Crack problems in the classical theory of elasticity 1969, John Wiley & Sons, New York (NY).
5. Martynenko M.A., Ulitko A.F. Stress state near the vertex of a spherical notch in an unbounded elastic medium. Soviet Appl Mech 1979, 14:911-918.
6. Martin P.A. On wrinkled penny-shaped cracks. J Mech Phys Solids 2001, 49:1481-1495.
7. Martin P.A. The spherical-cap crack revisited. Int J Solids Struct 2001, 38:4759-4776.
8. Lai Y.-S., Movchan A.B., Rodin G.J. A study of quasi-circular cracks. Int J Fract 2002, 113:1-25.
9. Kasano H., Matsumoto H., Nakahara I. A torsion-free axisymmetric problem of a cylindrical crack in a transversely isotopic body. Bull Jpn Soc Mech Engng 1984, 27:1323-1332.
10. Farris T.N., Kokini K., Demir I. The cylindrical crack. ASME J Appl Mech 1989, 56:981-983.
11. Demir I., Hirth J.P., Zbib H.M. The extended stress field around a cylindrical crack using the theory of dislocation pile-ups. Int J Engng Sci 1992, 30:829-845.
12. Hills D.A., Kelly P.A., Dai D.N., Korsunsky A.M. Solution of crack problems. The distributed dislocation technique, Volume 44, Series solid mechanics and its applications 1996, Kluwer Academic Publ., Dordrecht.
13. Zhang X., Detournay E., Jeffrey R.G. Propagation of a penny-shaped hydraulic fracture parallel to the free-surface of an elastic half-space. Int J Fract 2002, 115:125-158.
14. Paynter R.J.H., Hills D.A., Sackfield A. The penny crack beneath the surface of a half-space: with application to the blister test. Int J Fract 2006, 142:173-182.
15. Gordeliy E., Detournay E. Displacement discontinuity method for modeling axisymmetric cracks in an elastic half-space. Int J Solids Struct 2011, 48(19):2614-2629.
16. Gordeliy E., Detournay E. Paper: "Theoretical analysis of Hertzian contact fracture: Ring crack" by Xu-Yue Wang, Lawrence Kwok-Yan Li, Yiu-Wing Mai, Yao-Gen Shen; Engineering Fracture Mechanics 75 (2008) 4247-4256. Engng Fract Mech 2011, 78:446-447.
17. Carpinteri A., Chiaia B., Invernizzi S. Numerical analysis of indentation fracture in quasi-brittle materials. Engng Fract Mech 2004, 71:567-577.
18. Sher E.N., Mikhailov A.M. Modeling the axially symmetric crack growth under blasting and hydrofracturing near free surface. J Min Sci 2008, 44(5).
19. Piccinin R., Ballarini R., Cattaneo S. Linear elastic fracture mechanics pullout analyses of headed anchors in stressed concrete. J Engng Mech June 2010, 136(6):761-768.
20. FRANC-2D. Cornell fracture group home page. Ithaca (NY): Cornell University; 1997. http://www.cfg.cornell.edu/software/software.htm.
21. Napier J.A.L., Malan D.F. The computational analysis of shallow depth tabular mining problems. J S Afr Inst Min Metall 2007, 107:725-742.
22. Napier JAL. Explicit discontinuity modeling of deep mine stope face and pillar foundation failure. In: Proceedings of the 45th US rock mechanics/geomechanics symposium, number 11-476. American Rock Mechanics Association; 2011.
23. Crouch S.L. Solution of plane elasticity problems by the displacement discontinuity method. Int J Numer Meth Engng 1976, 10:301-343.
24. Crouch S.L., Starfield A.M. Boundary element methods in solid mechanics 1983, George Allen and Unwin, London.
25. Ryder JA, Napier JAL. Error analysis and design of a large-scale tabular mining stress analyzer. In: Proceedings of the 5th international conference on numerical methods in geomechanics, Nagoya; 1985. p. 1549-55.
26. Gordeliy E., Detournay E. A fixed grid algorithm for simulating the propagation of a shallow hydraulic fracture with a fluid lag. Int J Numer Anal Methods Geomech 2011, 35(5):602-629.
27. Barsoum R.S. On the use of isoparametric finite elements in linear fracture mechanics. Int J Numer Methods Engng 1976, 10(1):25-37.
28. Erdogan F., Sih G.C. On the crack extension in plates under plate loading and transverse shear. J Basic Engng 1963, 85:519-527.
29. Gordeliy E, Detournay E, Napier JAL. Modeling of near-surface bowl-shaped fractures. In: Proceedings of the 44th US rock mechanics symposium, number 10-155. American Rock Mechanics Association; 2010.
30. Mogilevskaya S.G. Numerical modeling of 2-d smooth crack growth. Int J Fract 1997, 87:389-405.