Bound theorem and implementation of dual finite elements for fracture assessment of piezoelectric materials

Computational Mechanics

Volumn 36, Issue 3, 2005, Pages 209-216

  Li, Z R ^a   Lim, C W ^a   Wu, C C ^a  

^a NONE

Author keywords

Bound theorem; Dual finite elements; Fracture assessment; Piezoelectric

Indexed keywords

COMPUTER SIMULATION; DIFFERENTIAL EQUATIONS; ELECTROMECHANICAL DEVICES; FINITE ELEMENT METHOD; FRACTURE; MATHEMATICAL MODELS; THEOREM PROVING;

BOUND THEOREM; DUAL FINITE ELEMENTS; FRACTURE ASSESSMENT; PIEZOELECTRIC;

PIEZOELECTRIC MATERIALS;

EID: 21644484856     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-004-0655-0     Document Type: Article

References (25)

1. McMeeking RM (1990) A J-integral for the analysis of electrically induced mechanical stress at cracks in elastic dielectrics. Int J Eng Sci 28: 605-613
2. Gao HJ, Zhang TY, Tong P (1997) Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic. J Mech Phys Solids 45: 491-510
3. Pak YE (1990) Crack extension force in a piezoelectric material. J Appl Mech 57: 647-653
4. Pak YE, Tobin A (1993) On electric field effects in fracture of piezoelectric materials. Mechanics of Electromagnetic Materials and Structures. AMD-vol. 161/MD-vol.42. ASME, New York
5. Park SB, Sun CT (1995) Fracture criteria for piezoelectric ceramics. J Am Ceram Soc 78: 1475-1480
6. Zhang, TY, Zhao, MH, Tong, P (2002) Fracture of piezoelectric ceramics, Adv. in Appl Mech 38: 147-289
7. Suo Z, Kuo CM, Barnett DM, Willis JR (1992) Fracture mechanics in piezoelectric material. J Mech Phys Solids 40: 739-765
8. Spyropoulos CP (2004) Energy release rate and path independent integral study for piezoelectric material with crack. Int J Solids & Structures. 41: 907-921
9. Kumar S, Singh RN (1996) Crack propagation in piezoelectric materials under combined mechanical and electrical loadings. Acta Mater. 44: 173-200
10. Kumar S, Singh RN (1997) Energy release rate and crack propagation in piezoelectric materials. Part I: mechanical/electrical load, Part II: combined mechanical and electrical loads. Acta Mater. 45: 849-868
11. Kuna M (1998) Finite element analyses of crack problems in piezoelectric structures. Comp Mater Sci 13: 67-80
12. Abendroth M, Groh U, Kuna M, Ricoeur A (2002) Finite element computation of the electromechanical J-Integral for 2D and 3D crack analysis. Int J Frac 114: 359-378
13. Wu CC, Sze KY, Huang YQ (2001) Numerical solutions on fracture of piezoelectric materials by hybrid element. Int J Solids & Structures 38: 4315-4329
14. Bui HD (1974) Dual path independent integrals in the boundary value problems of cracks. Eng Frac Mech 6: 287-296
15. Li X (1992) Conservation laws and dual conservation laws for cracks problems in honmogeneous isotropic conductive solids. Eng Frac Mech 42: 51-57
16. Wu CC, Xiao QZ, Yagawa G (1998) Dual analysis for path integrals and bounds for crack parameter. Int J Solids & Structures 35: 1635-1652
17. Wu CC, Xiao QZ, Li ZR (1999) Fracture estimation: bound theorem and numerical strategy. Comput Meth in Struct Eng Cheng FY, Gu YX. (eds.) 349-360, Elsevier
18. Sze KY, Wu CC, Huang YQ (1999) Upper and lower bounds for evaluation of nonlinear fracture parameters. Int J Eng Fracture Mechanics 62: 185-201
19. Liu M (1998) Finite Element Analysis for Cracked Piezoelectric Medium. M. Se. Thesis, Dept. of Modern Mechanics, Univ. of Sci. & Tech. of China, Hefei
20. Pak YE (1992) Linear electro-elastic fracture mechanics of piezoelectric materials. Int J Frac 54: 79-100
21. Parton VZ (1976) Fracture mechanics of piezoelectric materials. Acta Astronaut 3: 671-683
22. Deeg WF (1980) The analysis of dislocation, crack and inclusion problems in piezoelectric solids, Ph.D. dissertation. Stanford University, CA
23. Pian THH, Sumihara K (1984) Rational approach for assumed stress finite elements. Int J Numer Methods Engrg 20: 1685-1695
24. Pian THH, Wu CC (1988) A rational approach for choosing stress term for hybrid finite element formulations. Int J Numer Methods Engrg 26: 2331-2343
25. Wu CC, Cheung YK (1995) On optimization approach of hybrid stress elements, Finite Elements in Analysis & Design 21: 111-128