JOURNAL BROWSE
Search
Advanced SearchSearch Tips
Computation of 2-D mixed-mode stress intensity factors by Petrov-Galerkin natural element method
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
Computation of 2-D mixed-mode stress intensity factors by Petrov-Galerkin natural element method
Cho, Jin-Rae;
 Abstract
The mixed-mode stress intensity factors of 2-D angled cracks are evaluated by Petrov-Galerkin natural element (PG-NE) method in which Voronoi polygon-based Laplace interpolation functions and CS-FE basis functions are used for the trial and test functions respectively. The interaction integral is implemented in a frame of PG-NE method in which the weighting function defined over a crack-tip integral domain is interpolated by Laplace interpolation functions. Two Cartesian coordinate systems are employed and the displacement, strains and stresses which are solved in the grid-oriented coordinate system are transformed to the other coordinate system aligned to the angled crack. The present method is validated through the numerical experiments with the angled edge and center cracks, and the numerical accuracy is examined with respect to the grid density, crack length and angle. Also, the stress intensity factors obtained by the present method are compared with other numerical methods and the exact solution. It is observed from the numerical results that the present method successfully and accurately evaluates the mixed-mode stress intensity factors of 2-D angled cracks for various crack lengths and crack angles.
 Keywords
2-D angled crack;mixed-mode stress intensity factor (SIF);interaction integral;Petrov-Galerkin natural element (PG-NE) method;crack length and angle;
 Language
English
 Cited by
 References
1.
Anderson, T.L. (1991), Fracture Mechanics: Fundamentals and Applications, 1st Edition, CRC Press.

2.
Babuska, I. and Melenk, J.M. (1997), "The partition of unity method", Int. J. Numer. Meth. Eng., 40, 727-758. crossref(new window)

3.
Barsoum, R.S. (1976), "On the use of isoparametric finite elements in linear fracture mechanics", Int. J. Numer. Meth. Eng., 10, 25-38. crossref(new window)

4.
Belytschko, T., Lu, Y.Y., Gu, L. and Tabbara, M. (1995), "Element-free Galerkin methods for static and dynamic fracture", Int. J. Solid. Struct., 32(17-18), 2547-2570. crossref(new window)

5.
Bhardwaj, G., Singh, I.V. and Mishra, B.K. (2015), "Stochastic fatigue crack growth simulation of interfacical crack in bi-layered FGMs using XIGA", Comput. Meth. Appl. Mech. Eng., 284, 186-229. crossref(new window)

6.
Braun, J. and Sambridge, M. (1995), "A numerical method for solving partial differential equations on highly irregular evolving grids", Nature, 376, 655-660. crossref(new window)

7.
Cherepanov, G.P. (1967), "The propagation of cracks in a continuous medium", J. Appl. Math. Mech., 31(3), 503-512. crossref(new window)

8.
Chinesta, F., Cescotto, S., Cueto, E. and Lorong, P. (2011), Natural Element Method for the Simulation of Structures and Processes, John Wiley & Sons, New Jersey.

9.
Ching, H.K. and Batra, R.C. (2001), "Determination of crack tip fields in linear elastostatics by the meshless local Petrov-Galerkin (MLPG) method", Comput. Model. Eng. Sci., 2(2), 273-289.

10.
Cho, J.R. and Lee, H.W. (2006a), "A Petrov-Galerkin natural element method securing the numerical integration accuracy", J. Mech. Sci. Tech., 20(1), 94-109. crossref(new window)

11.
Cho, J.R. and Lee, H.W. (2006b), "2-D large deformation analysis of nearly incompressible body by natural element method", Comput. Struct., 84, 293-304. crossref(new window)

12.
Cho, J.R. and Lee, H.W. (2007), "2-D frictionless dynamic contact analysis of large deformable bodies by Petrov-Galerkin natural element method", Comput. Struct., 85, 1230-1242. crossref(new window)

13.
Cho, J.R., Lee, H.W. and Yoo, W.S. (2013), "Natural element approximation of Reissner-Mindlin plate for locking-free numerical analysis of plate-like thin elastic structures", Comput. Meth. Appl. Mech. Eng., 256, 17-28. crossref(new window)

14.
Cho, J.R. and Lee, H.W. (2014), "Calculation of stress intensity factors in 2-D linear fracture mechanics by Petrov-Galerkin natural element method", Int. J. Numer. Meth. Eng., 98, 819-839. crossref(new window)

15.
Dolbow, J. and Gosz, M. (2002), "On the computation of mixed-mode stress intensity factors in functionally graded materials", Int. J. Solid. Struct., 39(9), 2557-2574. crossref(new window)

16.
Fan, S.C., Liu, X. and Lee, C.K. (2004), "Enriched partition-of-unity finite element method for stress intensity factors at crack tips", Comput. Struct., 82, 445-461. crossref(new window)

17.
Fleming, M., Chu, Y.A., Moran, B. and Belytschko, T. (1997), "Enriched element-free Galerkin methods for crack tip fields", Int. J. Numer. Meth. Eng., 40, 1483-1504. crossref(new window)

18.
Henshell, R.D. and Shaw, K.G. (1975), "Crack tip elements are unnecessary", Int. J. Numer. Meth. Eng., 9, 495-507. crossref(new window)

19.
Hibbitt, H.D. (1977), "Some properties of singular isoparametric elements", Int. J. Numer. Meth. Eng., 11, 180-184. crossref(new window)

20.
Irwin, G.R. (1957), "Analysis of stresses and strains near the end of a crack traveling a plate", J. Appl. Mech., 24, 361-364.

21.
Liu, X.Y., Xiao, Q.Z. and Karihaloo, B.L. (2004), "XFEM for direct evaluation of mixed mode SIFs in homogeneous and bi-materials", Int. J. Numer. Meth. Eng., 59, 1103-1118. crossref(new window)

22.
Moes, N., Dolbow, J. and Belytschko, T. (1999), "A finite element method for crack growth without remeshing", Int. J. Numer. Meth. Eng., 46, 131-150. crossref(new window)

23.
Nie, Z.F., Zhou, S.J., Han, R.J., Xiao, L.J. and Wang, K. (2011), " $C^1$ natural element method for strain gradient linear elasticity and its application to microstructures", Acta Mechanica Sinica, 28(1), 91-103.

24.
Pant, M., Singh, I.V. and Mishra, B.K. (2011), "A novel enrichment criterion for modeling kinked cracks using element free Galerkin method", Int. J. Mech. Sci., 68, 140-149.

25.
Pena, E., Martinez, M.A., Calvo, B. and Doblare, M. (2008), "Application of the natural element method to finite deformation inelastic problems in isotropic and fiber-reinforced biological soft tissues", Comput. Meth. Appl. Mech. Eng., 197(21-24), 1983-1996. crossref(new window)

26.
Rabczuk, T. and Belytschko, T. (2004), "Cracking particles: a simplified meshfree method for arbitrary evolving cracks", Int. J. Numer. Meth. Eng., 61, 2316-2343. crossref(new window)

27.
Rao, B.N. and Rahman, S. (2000), "An efficient meshless method for fracture analysis of cracks", Comput. Mech., 26, 398-408. crossref(new window)

28.
Rice, J.R. (1968), "A path independent integral and the approximate analysis of strain concentration by notches and cracks", J. Appl. Mech., 35, 379-386. crossref(new window)

29.
Rice, J.R. and Tracey, D.M. (1973), Computational fracture mechanics. Numerical and Computer Methods in Structural Mechanics, Eds. Fenves, S.J. et al., Academic Press.

30.
Rooke, D.O. and Cartwright, D.J. (1976), Compendium of Stress Intensity Factors, The Hillingdon Press.

31.
Shi, J., Ma, W. and Li, N. (2013), "Extended meshless method based on partition of unity for solving multiple crack problems", Meccanica, 43(9), 2263-2270.

32.
Singh, I.V., Mishra, B.K., Bhattacharya, S. and Patil, R.U. (2012), "The numerical simulation of fatigue crack growth using extended finite element method", Int. J. Fatig., 36, 109-119. crossref(new window)

33.
Strang, G. and Fix, G.J. (1973), An Analysis of the Finite Element Method, Prentice-Hall, New Jersey.

34.
Sukumar, N., Moran, B. and Belytschko, T. (1998), "The natural element method in solid mechanics", Int. J. Numer. Meth. Eng., 43, 839-887. crossref(new window)

35.
Tong, P., Pian, T.H.H. and Lasry, S.J. (1973), "A hybrid element approach to crack problems in plane elasticity", Int. J. Numer. Meth. Eng., 7, 297-308. crossref(new window)

36.
Xiao, Q.Z., B.L. Karihaloo, B.L. and Liu, X.Y. (2004), "Direct determination of SIF and higher order terms of mixed mode cracks by a hybrid crack element", Int. J. Fract., 125, 207-225. crossref(new window)

37.
Yau, J.F., Wang, S.S. and Corten, H.T. (1980), "A mixed-mode crack analysis of isotropic solids using conservation laws of elasticity", J. Appl. Mech., 47, 335-341. crossref(new window)

38.
Yvonnet, J., Ryckelynck, D., Lorong, P. and Chinesta, F. (2004), "A new extension of the natural element method for non-convex and discontinuous problems: the constrained natural element method (C-NEM)", Int. J. Numer. Meth. Eng., 60(8), 1451-1474. crossref(new window)

39.
Zhang, Z., Liew, K.M., Cheng, Y. and Lee, Y.Y. (2008), "Analyzing 2D fracture problems with the improved element-free Galerkin method", Eng. Anal. Bound. Elem., 32, 241-250. crossref(new window)