Dynamic crack propagation with cohesive elements: A methodology to address mesh dependency

International Journal for Numerical Methods in Engineering

Volumn 59, Issue 1, 2004, Pages 1-24

  Zhou, F ^a   Molinari, J F ^a  

^a Johns Hopkins University   (United States)

Author keywords

Brittle materials; Cohesive elements; Dynamic fracture; Monte Carlo simulations; Weibull

Indexed keywords

BRITTLE FRACTURE; CERAMIC PRODUCTS; COMPUTER SIMULATION; ELASTIC MODULI; FINITE ELEMENT METHOD; LOADING; MONTE CARLO METHODS; PROBLEM SOLVING; RINGS (COMPONENTS);

CERAMIC RINGS; CRACK BRANCHING;

CRACK PROPAGATION;

CRACK PROPAGATION; NUMERICAL MODEL;

EID: 0347765706     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.857     Document Type: Article

References (43)

1. Daux C. Moes N. Dolbow J. Belytschko T. Arbitrary branched and intersecting cracks with the extended finite element method. International Journal for Numerical Methods in Engineering 2000; 48:1741-1760.
2. Fleming M, Chu Y, Moran B, Belytschko T. Enriched element-free Galerkin methods for crack tip fields. International Journal for Numerical Methods in Engineering 1997; 40(8):1483-1504.
3. Johnson GR, Holmquist TJ. A computational constitutive model for brittle materials subjected to large strains, high strain rates, and high pressures. In Shock-Wave and High-Strain Rate Phenomena in Materials, Meyers MA, Murr LE, Standhammer KP (eds). Marcel Dekker: New York, 1992; 1075-1081.
4. Curran DR, Seaman L, Cooper T, Shockey DA. Micromechanical model for comminution and granular flow of brittle material under high strain rate application to penetration of ceramic targets. International Journal of Impact Engineering 1993; 13:53-83.
5. Dugdale DS. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 1960; 8:100-104.
6. Barrenblatt GI. The mathematical theory of equilibrium of cracks in brittle fracture. Advances in Applied Mechanics 1962: 7:55-129.
7. Rice JR. Mathematical analysis in the mechanics of fracture. In Fracture, Liebowitz H (ed.). Academic Press: New York, 1968; 191-311.
8. Hillerborg A, Modeer M, Petersson PE, Needleman A. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Research 1976; 6:773-782.
9. Rose JH, Ferrante J, Smith JR. Universal binding energy curves for metals and bimetallic interfaces. Physical Review Letters 1981; 47(9):675-678.
10. Needleman A. A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics 1987; 54:525-531.
11. Ortiz M. Microcrack coalescence and macroscopic crack growth initiation in brittle solids. International Journal of Solids and Structures 1988; 24:231-250.
12. Ortiz M. Computational micromechanics. Computational Mechanics 1996: 18:321-338.
13. Camacho GT, Ortiz M. Computational modelling of impact damage in brittle materials. International Journal of Solids and Structures 1996; 33(20-22):2899-2938.
14. Ortiz M, Pandolfi A. Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. International Journal for Numerical Methods in Engineering 1999; 44(9):1267-1282.
15. Tvergaard V, Hutchinson JW. Effect of strain dependent cohesive zone model on predictions of interface crack growth. Journal de Physique IV 1996; 6:165-172.
16. Xu XP, Needleman A. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 1994; 42:1397-1434.
17. Xu XP, Needleman A. Numerical simulations of dynamic interfacial crack growth allowing for crack growth away from the bond line. International Journal of Fracture 1995: 74:253-275.
18. Xu XP, Needleman A. Numerical simulations of dynamic crack growth along an interface. International Journal of Fracture 1996; 74:289-324.
19. Pandolfi A, Krysl P, Ortiz M. Finite element simulation of ring expansion and fragmentation. International Journal of Fracture 1999; 95(1-4):279-297.
20. Pandolfi A, Guduru PR, Ortiz M, Rosakis AJ. Finite element analysis of experiments of dynamic fracture in c300 steel. International Journal of Solids and Structures 2000; 37(27):3733-3760.
21. Pandolfi A, Ortiz M. An efficient adaptive procedure for three-dimensional fragmentation simulations. Engineering with Computers 2002; 18:148-159.
22. Ruiz G, Pandolfi A, Ortiz M. Three-dimensional finite element simulation of dynamic brazilian tests on concrete cylinders. International Journal for Numerical Methods in Engineering 2000; 48(7):963-994.
23. Nguyen O, Repetto EA, Ortiz M, Radovitzky RA. A cohesive model of fatigue crack growth. International Journal of Fracture 2001; 110(4):351-369.
24. Chengxiang Yu. Three-Dimensional Cohesive Modeling of Impact Damage of Composites. Ph.D. Thesis, California Institute of Technology, Pasadena, California, May 2001.
25. Weibull W. The phenomenon of rupture in solids. Proceedings of the Royal Academy of Engineering Sciences, vol. 153, Stockholm, Sweden, 1939.
26. W. Weibull. A statistical distribution function of wide applicability. Journal of Applied Mechanics 1951; 18: 293-297.
27. Bazant, ZP. Size effect on structural strength: a review. Archive of Applied Mechanics 1999; 69(9-10):703-725.
28. Bazant, ZP, Chen. E-P. Scaling of structural failure. Applied Mechanics Reviews (ASME) 1997; 50:593-627.
29. Zavattieri PD, Raghuram PV, Espinosa HD. A computational model of ceramic microstructures subjected to multi-axial dynamic loading. Journal of the Mechanics and Physics of Solids 2000; 49(1):27-68.
30. Zavattieri PD, Espinosa HD. Grain level analysis of crack initiation and propagation in brittle materials. Acta Materiala 2001; 49:4291-4311.
31. Lubliner J. On the thermodynamic foundations of non-linear solid mechanics. International Journal of Non-Linear Mechanics 1972; 7:237-254.
32. Lubliner J. On the structure of the rate equations of materials with internal variables. Acta Mechanica 1973; 17:109-119.
33. Hughes TJR. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Prentice-Hall: Englewood Cliffs, NJ, 1987.
34. Belytschko T. An overview of semidiscretization and time integration procedures. In Belytschko, T, Hughes, TJR (eds). Computational Methods for Transient Analysis. North-Holland: Amsterdam, 1983; 1-65.
35. Hashimoto R, Ogawa A, Morimoto T, Yonaiyama M. Spin tests of silicon nitride disk. 74th Japan Society of Mechanical Engineering Fall Annual Conference, Kyoto, Japan, 21-23 September 1996, vol. 2, 441-442.
36. Shioya T, Zhou F. Dynamic fracture toughness and crack propagation in brittle materials. In IUTAM Symposium on Constitutive Relation in High/very high Strain Rates, Noda, Japan, October 1995; 105-112.
37. Satoh H. On the crack propagation in brittle materials. Thesis, Department of Aeronautics and Astronautic, University of Tokyo, Japan, 1996.
38. Weibull W. A statistical theory of the strength of materials. Proceedings of the Royal Academy of Engineering Sciences, vol. 151, Stockholm, Sweden, 1939.
39. Ruiz G, Pandolfi A, Ortiz M. Three-dimensional cohesive modeling of dynamic mixed mode fracture. International Journal for Numerical Method in Engineering 2001; 52:97-120.
40. Xue Q, Meyers MA, Nesterenko VF. Self-organization of shear bands in titanium and Ti-6A1-4V alloy. Acta Materiala 2002; 50(3):575-596.
41. Meyers MA, Nesterenko VF, LaSalvia JC, Xue Q. Shear localization in dynamic deformation of materials: microstructural evolution and self-organization. Materials Science and Engineering A 2001; 317(1-2):204-225.
42. Nesterenko VF, Xue Q, Meyers MA. Self-organization of shear bands in Ti, Ti-6A1-4V, and 304 stainless steel. Journal de Physique IV 2000; 10(P9):269-274.
43. Nemat-Nasser S, Keer LM, Parihar KS. Unstable crack growth of thermally induced interacting cracks in brittle solids. International Journal of Solids and Structures 1978; 14(6):409-439.