Evaluation of elastic-plastic crack tip parameters using partition of unity finite element method and pseudo elastic analysis

CMES - Computer Modeling in Engineering and Sciences

Volumn 39, Issue 1, 2009, Pages 67-99

  Sethuraman, Raju ^a   Rajesh, N R ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY MADRAS   (India)

Author keywords

Effective material parameters; Elastic plastic; HRR singularity; J integral; Partition of unity finite element method; Pseudo elastic analysis

Indexed keywords

CRACK DETECTION; CRACK TIPS; DEFORMATION; ELASTOPLASTICITY; PLASTICS; TENSILE TESTING;

EFFECTIVE MATERIAL PARAMETERS; ELASTIC-PLASTIC; HRR SINGULARITY; J-INTEGRAL; PARTITION OF UNITY FINITE ELEMENT METHOD; PSEUDO ELASTIC ANALYSIS;

FINITE ELEMENT METHOD;

EID: 63349106498     PISSN: 15261492     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (36)

1. st ed. (CRC Press, FL).
2. ANSYS Release 8.0. (2000): Structural analysis guide. (ANSYS Inc. Canonburg, PA).
3. Atluri, S. N.; Nishioka, T.; Nakagaki, M. (1984): Incremental path-independent integrals in inelastic and dynamic fracture mechanics, Eng. Fract. Mech., vol. 20, no. 2, pp. 209-244.
4. Atluri, S. N.; Zhu, T. (1998): A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech., vol. 22, pp. 117-127.
5. Atluri, S. N. (2004): The meshless local Petrov-Galerkin (MLPG) method for domain & boundary discretizations. Tech Science Press.
6. Bradford, R. (1984): Persistence of the HRR fields for general yielding in mode-II. Int. J. Fract., vol. 26, pp. 85-98.
7. Cai, Y.C; Zhu, H.H. (2008): A local meshless Shepard and least square interpolation method based on local weak form. CMES: Computer Modeling in Engineering & Sciences, vol. 34, no. 2, pp. 179-204.
8. Chen, W.-H.; Chen, C.-H. (2005): On three-dimensional fracture mechanics analysis by an enriched meshless method. CMES: Computer Modeling in Engineering & Sciences, vol. 8, no. 3, pp. 177-190.
9. Dai, K. Y.; Liu, G. R.; Han, X.; Li, Y. (2006): Inelastic analysis of 2D solids using a weak form RPIM based on deformation theory. Comput. Methods Appl. Mech. Engrg., vol. 195, pp. 4179-4193.
10. Desikan, V.; Raju Sethuraman (2000): Analysis of material non-linear problems using pseudo-elastic finite element method. J. Pressure Vessel Technol., vol. 122, pp. 457-461.
11. Duarte, C. A.; Babuska, I.; Oden, J. T. (2000): Generalized finite element methods for three-dimensional structural mechanics problems. Comput. Struct., vol. 77, pp. 215-232.
12. Elguedj, T.; Gravouil, A.; Combescure, A. (2006): Appropriate extended functions for X-FEM simulation of plastic fracture mechanics. Comput. Methods Appl. Mech. Engrg., vol. 195, pp. 501-515.
13. Fan, S. C.; Liu, X.; Lee, C. K. (2004): Enriched partition of unity finite element method for stress intensity factors at crack tips. Comput. Struct., vol. 82, pp. 445-461.
14. Fleming, M.; Chu, Y. A.; Moran, B.; Belytschko, T.; Lu, Y. Y.; Gu, L. (1997): Enriched element free Galerkin methods for crack tip fields. Int. J. Numer. Methods Eng., vol. 40, pp. 1483-1504.
15. Hagihara, S.; Tsunori, M.; Ikeda, T.; Miyazaki, N (2007): Application of meshfree method to elastic-plastic fracture mechanics parameter analysis. CMES: Computer Modeling in Engineering & Sciences, vol. 17, no. 2, pp. 63-72.
16. Han, Z.D.; Atluri, S. N. (2004): Meshless local Petrov-Galerkin (MLPG) approaches for solving 3D Problems in elasto-statics. CMES: Computer Modeling in Engineering & Sciences, vol. 6, no. 2, pp. 169-188.
17. Han, Z.D.; Rajendran, A.M.; Atluri, S. N. (2005): Meshless local Petrov-Galerkin (MLPG) approaches for solving nonlinear problems with large deformations and rotations. CMES: Computer Modeling in Engineering & Sciences, vol. 10, no. 1, pp. 1-12.
18. Hutchinson, J. W. (1968a): Singular behaviour at end of a tensile crack in a hardening material. J. Mech. Phys. Solids, vol. 16, pp. 13-31.
19. Hutchinson, J. W. (1968b): Plastic stress and strain fields at a crack tip. J. Mech. Phys. Solids, vol. 16, pp. 337-347.
20. Li, L.; Liu, S.; Wang, H. (2008): Meshless analysis of ductile failure. CMES: Computer Modeling in Engineering & Sciences, vol. 36, no. 2, pp. 173-191.
21. Long, S.Y.; Liu, K.Y.; Li, G.Y. (2008): An analysis for the elasto-plastic fracture problem by the meshless local Petrov-Galerkin method. CMES: Computer Modeling in Engineering & Sciences, vol. 28, no. 3, pp. 203-216.
22. Melenk, J. M.; Babuska, I. (1996): The partition of unity finite element method: basic theory and applications. Comput. Methods Appl. Mech. Engrg., vol. 139, pp. 289-314.
23. Moes, N.; John Dolbow; Ted Belytschko (1999): A finite element method for crack growth without remeshing. Int. J. Numer. Methods Eng., vol. 46, pp. 131-150.
24. Raju, I. S.; Shiva Kumar, K. N. (1990): An equivalent domain integral method in the two dimensional analysis of mixed mode crack problems. Eng. Fract. Mech., vol. 37(4), pp. 707-725.
25. Raju Sethuraman; Cherku Sridhar Reddy (2004): Pseudo elastic analysis of material non-linear problems using EFG method. Transactions of the Chinese Institute of Engineers, series A, vol. 27(4), pp. 505-516.
26. Raju Sethuraman; Cherku Sridhar Reddy (2008): Pseudo elastic analysis of elastic-plastic crack tip fields using element free Galerkin method. Int. J. Comput. Methods, vol. 5, pp. 91-117.
27. Rao, B. N.; Rahman, S. (2004): An enriched mesh less method for non-linear fracture mechanics. Int. J. Numer. Methods Eng., vol. 59, pp. 197-223.
28. Rice, J. R. (1968): A path independent integral and approximate analysis of strain concentrations by notches and cracks. J. Appl. Mech., vol. 51(2), pp. 379-386.
29. Rice, J. R.; Rosengren, G. F. (1968): Plane strain deformation near a crack tip in a power law hardening material. J. Mech. Phys. Solids, vol. 16, pp. 1-12.
30. Shih, C. F.; German, M. D. (1981): Requirements for one parameter characterization of crack tip fields by the HRR singularity. Int. J. Fract., vol. 17, pp. 27-43.
31. Shih, C. F. (1983): Tables of HRR singular field quantities, MRL E-147. Material Research Laboratory, Brown University, 1983.
32. Sladek, J.; Sladek, V.; Solek, P.; Atluri, S.N. (2008): Modeling of intelligent material systems by the MLPG. CMES: Computer Modeling in Engineering & Sciences, vol. 34, no. 3, pp. 273-300.
33. Sukumar, N.; Prévost, J. H. (2003): Modeling quasi-static crack growth with extended finite element method. Int. J. Solids Struct., vol. 40, pp. 7513-7537.
34. Strouboulis, T.; Babuska, I.; Copps, K. (2000): The design and analysis of the generalized finite element method. Comput. Methods Appl. Mech. Engrg., vol. 181, pp. 43-69.
35. Strouboulis, T.; Copps, K.; Babuska, I. (2001): The generalized finite element method. Comput. Methods Appl. Mech. Engrg., vol. 190, pp. 4081-4193.
36. Wen, P.H.; Aliabadi, M.H.; Liu, Y.W. (2008): Meshless method for crack analysis in functionally graded materials with enriched radial base functions. CMES: Computer Modeling in Engineering & Sciences, vol. 30, no. 3, pp. 133-147.