A damage model for crack prediction in brittle and quasi-brittle materials solved by the FFT method

International Journal of Fracture

Volumn 173, Issue 2, 2012, Pages 135-146

  Li, Jia ^a   Tian, Xiao Xiao ^b   Abdelmoula, Radhi ^a  

^a UNIVERSITÉ PARIS 13   (France)

^b HARBIN INSTITUTE OF TECHNOLOGY   (China)

Author keywords

Brittle materials; Crack growth; Damage; FFT; Fracture

Indexed keywords

CRACK PREDICTION; DAMAGE; DAMAGE GROWTH; DAMAGE MODEL; FAST FOURIER TRANSFORM (FFT); FRACTURE PROCESS; GRIFFITH CRITERION; NON-LOCAL DAMAGE; NONLOCAL MODELS; NUMERICAL SOLUTION; PRINCIPAL STRESS; QUASIBRITTLE MATERIAL;

CRACK PROPAGATION; FAST FOURIER TRANSFORMS; FRACTURE;

BRITTLENESS;

EID: 84862803008     PISSN: 03769429     EISSN: 15732673     Source Type: Journal    
DOI: 10.1007/s10704-011-9671-1     Document Type: Article

References (27)

1. N Bilger F Auslender M Bornert H Moulinec A Zaoui 2007 Bounds and estimates for the effective yield surface of porous media with a uniform or a nonuniform distribution of voids Euro J Mech A/Solids 26 810 836 10.1016/j.euromechsol.2007.01.004 (Pubitemid 47061431)
2. A Carpinteri F Ciola N Pugno 2001 Boundary element method for the strain-softening response of quasi-brittle materials in compression Comput Struct 79 389 401 10.1016/S0045-7949(00)00149-8
3. A Carpinteri GP Yang 1997 Size effects in brittle specimen with micro crack interaction Comput Struct 63 429 437 10.1016/S0045-7949(96)00362-8 (Pubitemid 127378204)
4. GJ Dienes A Paskin 1987 Molecular dynamic simulations of crack propagation J Phys Chem Solids 48 11 1015 1033 10.1016/0022-3697(87)90117-X (Pubitemid 18548134)
5. NE Frost 1959 A relation between the critical alternating propagation stress and crack length for mild steel Proc Inst Mech Eng 173 811 827 10.1243/PIME-PROC-1959-173-065-02
6. AA Griffith 1920 The phenomena of rupture and flow in solids Philos Trans R Soc Lond 221 163 198
7. MI Idiarta H Moulinec P Ponte Castaneda P Suquet 2006 Macroscopic behavior and field fluctuations in viscoplastic composites: Second-order estimates versus full-field simulations J Mech Phys Solids 54 1029 1063 10.1016/j.jmps.2005.11.004 (Pubitemid 43227864)
8. G Irwin 1968 Linear fracture mechanics, fracture transition and fracture control Eng Fract Mech 1 241 257 10.1016/0013-7944(68)90001-5
9. Karihaloo BL, Shao PF, Xiao QZ (2003) Lattice modelling of the failure of particle composites. Eng Fract Mech 70-2385-2406
10. Kitagawa H, Takahashi S (1976) Applicability of fracture mechanics to very small cracks or the cracks in the early stage. In: Proceedings of 2nd International Conference on mechanical behaviour of materials, Boston, pp 627-631
11. J Lankford 1986 The influence of microstructure on the growth of small fatigue crack Fatigue Fract Eng Mater Struct 8 161 175
12. RA Lebensohn EM Bringa A Caro 2007 A viscoplastic micromechanical model for the yield strength of nanocrystalline materials Acta Mater 55 261 271 10.1016/j.actamat.2006.07.023 1:CAS:528:DC%2BD28Xht1KhsrnI (Pubitemid 44820942)
13. RA Lebensohn Y Liu P Ponte Castañeda 2004 On the accuracy of the self-consistent approximation for polycrystals: comparison with full-field numerical simulations Acta Mater 52 5347 5361 10.1016/j.actamat.2004.07.040 1:CAS:528:DC%2BD2cXns1ertLs%3D
14. G Lilliu JGM van Mier 2003 3D lattice type fracture model for concrete Eng Fract Mech 70 927 941 10.1016/S0013-7944(02)00158-3 (Pubitemid 36196033)
15. WK Liu EG Karpov S Zhang HS Park 2004 An introduction to computational nano mechanics and materials Comput Methods Appl Mech Eng 193 1529 1578 10.1016/j.cma.2003.12.008 (Pubitemid 38472896)
16. JC Michel H Moulinec P Suquet 2000 Computational method based on augmented lagrangians and fast Fourier transforms for composites with high contrast Comput Model Eng Sci 1 2 79 88
17. JC Michel H Moulinec P Suquet 1999 Effective properties of composites materials with periodic microstructure: a computational approach Comput Methods Appl Mech Eng 172 109 143 10.1016/S0045-7825(98)00227-8
18. H Moulinec P Suquet 1994 A fast numerical method for computing the linear and the nonlinear mechanical properties of composites CR Acad Sci Paris Ser II 318 1417 1423
19. H Moulinec P Suquet 1998 A numerical method for computing the overall response of nonlinear composites with complex microstructure Comput Methods Appl Mech Eng 157 69 94 10.1016/S0045-7825(97)00218-1 (Pubitemid 128368551)
20. M Mullins 1982 Molecular dynamics simulation of propagating cracks Original Research Article Scr Metallurgica 16-6 663 666 10.1016/0036-9748(82) 90318-0 (Pubitemid 12520795)
21. TK Nguyen K Sab G Bonnet 2008 Green's operator for a periodic medium with traction-free boundary conditions and computation of the effective properties of thin plates Int J Solids Struct 45 6518 6534 10.1016/j.ijsolstr.2008.08.015
22. M Ostoja-Starzewski PY Sheng K Alzebdeh 1996 Spring network models in elasticity and fracture of composites and polycrystals Comput Mater Sci 7 82 93 10.1016/S0927-0256(96)00064-X (Pubitemid 126412331)
23. G Pijaudier-Cabot ZP Bazant 1987 Nonlocal damage theory J Eng Mech ASCE 113 1512 1533 10.1061/(ASCE)0733-9399(1987)113:10(1512)
24. Sih G (1973) Handbook of stress-intensity factors. Lehigh University, Bethlehem
25. ML Williams 1961 The bending stress distribution at the base of a stationary crack J Appl Mech 28 78 82 10.1115/1.3640470
26. XB Zhang J Li SE Boukha 2009 Modelling the failure behaviour of brittle or quasi-brittle materials by analyzing the growth of micro-cracks Int J Fract 160 73 83 10.1007/s10704-009-9412-x 1:CAS:528:DC%2BD1MXhtlKms7%2FI
27. R Zimbelmann 1985 A contribution to the problem of cement-aggregate bond Cem Conc Res 15 801 808 10.1016/0008-8846(85)90146-2 1:CAS:528: DyaL2MXlvVaks7w%3D (Pubitemid 15590191)