Modeling fracture in nanomaterials via a virtual internal bond method

Engineering Fracture Mechanics

Volumn 70, Issue 14, 2003, Pages 1777-1791

  Gao, Huajian ^a   Ji, Baohua ^a  

^a MAX PLANCK INSTITUTE FOR INTELLIGENT SYSTEMS   (Germany)

Author keywords

Cohesive zone; Fracture modeling; Nanomaterial; Size effect

Indexed keywords

CRACKS; DEFORMATION; FAILURE (MECHANICAL); INTERFACIAL ENERGY; NANOSTRUCTURED MATERIALS; NANOTECHNOLOGY; STRESS CONCENTRATION;

COHESIVE INTERACTIVE LAW;

FRACTURE MECHANICS;

FRACTURE MECHANICS; NANOPARTICLE;

EID: 0037927919     PISSN: 00137944     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0013-7944(03)00124-3     Document Type: Article

References (32)

1. Walsh P. Li W. Kalia R.K. Nakano A. Vashishta P. Saini S. Structural transformation, amorphization, and fracture in nanowires: a multimillion-atom molecular dynamics study Appl. Phys. Lett. 78 21 2001 3328-3330
2. Vaia R.A. Giannelis E.P. Polymer nanocomposites: status and opportunities MRS Bull. 26 2001 394-401
3. Stoneham A.M. The challenges of nanostructures for theory Mater. Sci. Engng. C 23 2003 235-241
4. Bao G. Mechanics of biomolecules J Mech Phys Solids 50 11 2002 2237-2274
5. Born M. Huang K. Dynamical theories of crystal lattices 1956 Clarendon Oxford
6. Huang K. On the atomic theory of elasticity Proc. Roy. Soc. Lond. A 203 1950 178-194
7. Stakgold I. The Cauchy relations in a molecular theory of elasticity Quart. Appl. Mech. 8 1950 169-186
8. Tadmor E.B. Ortiz M. Phillips R. Quasicontinuum analysis of defects in solids Philos. Mag. A 73 1996 1529-1563
9. Gao H. Klein P. Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds J. Mech. Phys. Solids 46 1998 187-218
10. Klein P. Gao H. Crack nucleation and growth as strain localization in a virtual-bond continuum Engng. Fract. Mech. 61 1998 21-48
11. Klein P. Foulk J.W. Chen E.P. Wimmer S.A. Gao H. Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods Theor. Appl. Fract. Mech. 37 2001 99-166
12. Milstein F. Review: theoretical elastic behavior at large strain J. Mater. Sci. 15 1980 1071-1084
13. Barenblatt G.I. The mathematical theory of equilibrium cracks in brittle fracture Adv. Appl. Mech. 7 1962 55-129
14. Dugdale D.S. Yielding of steel sheets containing slits J. Mech. Phys. Solids 8 1960 100-104
15. Hillerborg A. Modeer A. Petersson P.E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements Cement Concrete Res. 6 1976 773-782
16. Bazant Z.P. Instability, ductility and size effect in strain-softening concrete J. Engng. Mech. Div.--ASCE 102 1976 331-344
17. Bazant Z.P. Planas J. Fracture and size effect of concrete and other quasibrittle materials 1998 CRC Press Boca Raton (FL)
18. Bazant Z.P. Cedolin L. Blunt crack band propagation in finite element analysis J. Engng. Mech. Div.--ASCE 105 1979 297-315
19. Bazant Z.P. Cedolin L. Fracture mechanics of reinforced concrete J. Engng. Mech. Div.--ASCE 106 1980 1257-1306
20. Bazant Z.P. Cedolin L. Finite element modeling of crack band propagation J. Struct. Engng.--ASCE 109 1983 69-92
21. Cedolin L. Bazant Z.P. Effect of finite element choice in blunt crack band analysis Comput. Meth. Appl. Mech. Engng. 24 1980 305-316
22. Bazant ZP. Crack band model for fracture of geomaterials. In: Eisenstein Z, editor. Proceedings of the Fourth International Conference on Numerical Methods in Geomechanics, vol. 3, 1982. p. 1137-52
23. Bazant Z.P. Oh B.-H. Crack band theory for fracture of concrete Mater. Struct. 16 1983 155-177
24. Rice J.R. A path independent integral and the approximate analysis of stress concentration by notches and cracks J. Mech. Phys. Solids 40 1968 939-963
25. Eshelby J.D. Energy relations and the energy momentum tensor in continuum mechanics Inelastic behavior of solids 1970 McGraw-Hill New York
26. Bazant Z.P. Size effect in blunt fracture: concrete, rock, metal J. Engng. Mech.--ASCE 110 1984 518-535
27. Planas J. Elices M. Size effect in concrete structure: mathematical approximations and experimental validation Mazars J. Bazant Z.P. Cracking and damage, strain localization and size effect 1989 462-476 Elsevier Applied Science London
28. Planas J. Elices M. Anomalous structural size effect in cohesive materials like concrete Suprenant B.A. Serviceability and durability of construction materials vol. 2 1990 1345-1356 American Society of Civil Engineers (ASCE) New York
29. Planas J. Elices M. The influence of specimen size and material characteristic size on applicability of effective crack models van Mier J.G.M. Rots J.G. Bakker A. Fracture processes in concrete, rock and ceramics 1991 1345-1356 E-FN Spon London
30. Planas J. Elices M. Shrinkage eigenstress and structural size-effect Bazant Z.P. Fracture mechanics of concrete structures 1992 939-950 Elsevier Applied Science London
31. Bao G. Suo Z. Remarks of crack-bridging concepts Appl. Mech. Rev. 45 8 1992 355-366
32. Suo Z. Ho S. Gong X. Notch ductile-to-brittle transition due to localized inelastic band J. Engng. Mater. Technol. 105 1993 319-326