Analysis of concrete fracture using a novel cohesive crack method

Applied Mathematical Modelling

Volumn 34, Issue 12, 2010, Pages 4219-4231

  Dong, Y ^a   Wu, S ^a   Xu, S S ^a   Zhang, Y ^a   Fang, S ^a  

^a BEIJING UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Computational mechanics; Crack; EFG; Fracture; Material failure; Meshless

Indexed keywords

COHESIVE CRACKS; CONCRETE FRACTURE; CRACK SURFACES; DISCRETE CRACKS; FRACTURE MATERIALS; MATERIAL MODELS; MESH-LESS METHODS; MESHLESS; NON-LINEAR RESPONSE; OTHER DISCRETE; TENSION SOFTENING;

COMPUTATIONAL MECHANICS; FRACTURE; HIGH ENERGY PHYSICS; NUMERICAL ANALYSIS;

CRACKS;

EID: 77954027351     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2010.04.019     Document Type: Article

References (63)

1. Bazant Z.P., Oh B.H. Crack band theory for fracture in concrete. Mater. Struct. 1983, 16:155-177.
2. Hao S., Liu W.K., Klein P.A., Rosakis A.J. Modeling and simulation of intersonic crack growth. Int. J. Solids Struct. 2004, 41(7):1773-1799.
3. Papa E., Nappi A. Numerical modelling of masonry: a material model accounting for damage effects and plastic strains. Appl. Math. Model. 1997, 21(6):319-335.
4. Ray A., Tangirala S., Phoha S. Stochastic modeling of fatigue crack propagation. Appl. Math. Model. 1998, 22(3):197-204.
5. Jirasek M., Zimmermann T. Analysis of rotating crack model. J. Eng. Mech. 1998, 124:842-851.
6. Malvar L.J., Fourney M.E. A three dimensional application of the smeared crack approach. Eng. Fract. Mech. 1990, 35(1-3):251-260.
7. Dorgan J. A mixed finite element implementation of a gradient-enhanced coupled damage-plasticity model. Int. J. Damage Mech. 2006, 15:201-235.
8. Rabczuk T., Eibl J. Simulation of high velocity concrete fragmentation using SPH/MLSPH. Int. J. Numer. Methods Eng. 2003, 56:1421-1444.
9. Rabczuk T., Eibl J., Stempniewski L. Numerical analysis of high speed concrete fragmentation using a meshfree Lagrangian method. Eng. Fract. Mech. 2004, 71(4-6):547-556.
10. Rabczuk T., Eibl J. Numerical analysis of prestressed concrete beams using a coupled element free Galerkin/finite element method. Int. J. Solids Struct. 2004, 41(3-4):1061-1080.
11. Rabczuk T., Belytschko T. Adaptivity for structured meshfree particle methods in 2d and 3d. Int. J. Numer. Methods Eng. 2005, 63(11):1559-1582.
12. Rabczuk T., Akkermann J., Eibl J. A numerical model for reinforced concrete structures. Int. J. Solids Struct. 2005, 42(5-6):1327-1354.
13. Rabczuk T., Eibl J. Modelling dynamic failure of concrete with mesh-free methods. Int. J. Impact Eng. 2006, 32(11):1878-1897.
14. Abu Al-Rub R.K., Voyiadiis G.Z. A finite strain plastic damage model for high velocity impact using combined viscosity and gradient localization limiters. Part I: Theoretical formulation. Int. J. Damage Mech. 2006, 15:293-334.
15. Khan A.R., Al-Gadhib A.H., Baluch M.H. Elasto-damage model for high strength concrete subjected to multiaxial loading. Int. J. Damage Mech. 2007, 16:361-398.
16. Barenblatt G. The mathematical theory of equilibrium of cracks in brittle fracture. Adv. Appl. Fract. 1962, 7:55-129.
17. Hillerborg A., Modeer M., Peterson P.E. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement Concrete Res. 1976, 6:773-782.
18. Ortiz M., Leroy Y., Needleman A. Finite element method for localized failure analysis. Comput. Methods Appl. Mech. Eng. 1987, 61:189-213.
19. Xu X.-P., Needleman A. Numerical simulations of fast crack growth in brittle solids. J. Mech. Phys. Solids 1994, 42:1397-1434.
20. Carol I., Lopez C.M., Roa O. Micromechanical analysis of quasi-brittle materials using fracture-based interface elements. Int. J. Numer. Methods Eng. 1996, 52:193-215.
21. Galves J.C., Cervenka J., Cendon D.A., Saouma V. A discrete crack approach to normal/shear cracking of concrete. Cement Concrete Res. 2002, 32(10):1567-1585.
22. Lee K.M., Park J.H. A numerical model for elastic modulus of concrete considering interfacial transition zone. Cement Concrete Res. 2008, 38(3):396-402.
23. Rabczuk T., Zi G., Gerstenberger A., Wall W.A. A new crack tip element for the phantom node method with arbitrary cohesive cracks. Int. J. Numer. Methods Eng. 2008, 75:577-599.
24. T. Rabczuk, S. Bordas, G. Zi, On three-dimensional modelling of crack growth using partition of unity methods, Comput. Struct., in press, doi:10.1016/j.compstruc.2008.08.010.
25. Rabczuk T., Zi G., Bordas S., Nguyen-Xuan H. A geometrically nonlinear three dimensional cohesive crack method for reinforced concrete structures. Eng. Fract. Mech. 2008, 75:4740-4758.
26. Bolotin V.V. Fracture from the standpoint of nonlinear stability. Int. J. Non-linear Mech. 1994, 29(4):569-585.
27. Bazant Z.P., Belytschko T. Wave propagation in a strain softening bar: exact solution. J. Eng. Mech. ASCE 1985, 11:381-389.
28. Yang X.H., Chen C.Y., Hu Y.T. Damage analysis and fracture criteria for piezoelectric ceramics. Int. J. Non-linear Mech. 2005, 40(9):1204-1213.
29. Haussler-Combe U., Hartig J. Formulation and numerical implementation of a constitutive law for concrete with strain-based damage and plasticity. Int. J. Non-linear Mech. 2008, 43(5):399-415.
30. De Borst R. Modern domain-based discretization methods for damage and fractures. Int. J. Fract. 2006, 138(1-4):241-9738.
31. Organ D., Fleming M., Terry T., Belytschko T. Continuous meshless approximations for nonconvex bodies by diffraction and transparency. Comput. Mech. 1996, 18:225-235.
32. Hao S., Liu W.K., Chang C.T. Computer implementation of damage models by finite element and meshfree methods. Comput. Methods Appl. Mech. Eng. 2000, 187(3-4):401-440.
33. Hao S., Liu W.K., Qian D. Localization-induced band and cohesive model. J. Appl. Mech. - Trans. ASME 2000, 67(4):803-812.
34. Rabczuk T., Areias P.M.A., Belytschko T. A meshfree thin shell method for non-linear dynamic fracture. Int. J. Numer. Methods Eng. 2007, 72:524-548.
35. Li S., Simonson Bo C. Meshfree simulation of ductile crack propagation. Int. J. Comput. Methods Eng. Sci. Mech. 2003, 6:1-19.
36. Hao S., Liu W.K. Moving particle finite element method with super-convergence: nodal integration formulation and applications. Comput. Methods Appl. Mech. Eng. 2006, 195(44-47):6059-6072.
37. Bordas S., Rabczuk T., Zi G. Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by extrinsic discontinuous enrichment of meshfree methods without asymptotic enrichment. Eng. Fract. Mech. 2008, 75:943-960.
38. Rabczuk T., Bordas S., Zi G. A three-dimensional meshfree method for continuous multiple crack initiation, nucleation and propagation in statics and dynamics. Comput. Mech. 2007, 40(3):473-495.
39. Rabczuk T., Areias P. A meshfree thin shell for arbitrary evolving cracks based on an extrinsic basis. Comput. Model. Eng. Sci. 2006, 16(2):115-130.
40. Rabczuk T., Gracie R., Song J.-H., Belytschko T. Immersed particle method for fluid-structure interaction. Int. J. Numer. Methods Eng. 2010, 81:48-71.
41. Rabczuk T., Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int. J. Numer. Methods Eng. 2004, 61(13):2316-2343.
42. Rabczuk T., Belytschko T. Application of particle methods to static fracture of reinforced concrete structures. Int. J. Fract. 2006, 137(1-4):19-49.
43. Rabczuk T., Areias P.M.A. A new approach for modelling slip lines in geological materials with cohesive models. Int. J. Numer. Anal. Methods Geomech. 2006, 30(11):1159-1172.
44. Rabczuk T., Belytschko T. A three dimensional large deformation meshfree method for arbitrary evolving cracks. Comput. Methods Appl. Mech. Eng. 2007, 196:2777-2799.
45. Rabczuk T., Areias P.M.A., Belytschko T. A simplified meshfree method for shear bands with cohesive surfaces. Int. J. Numer. Methods Eng. 2007, 69(5):993-1021.
46. Rabczuk T., Samaniego E. Discontinuous modelling of shear bands using adaptive meshfree methods. Comput. Methods Appl. Mech. Eng. 2008, 197:641-658.
47. Rabczuk T., Song J.-H., Belytschko T. Simulations of instability in dynamic fracture by the cracking particles method. Eng. Fract. Mech. 2009, 76:730-741.
48. Belytschko T., Lu Y.Y., Gu L. Element-free Galerkin methods. Int. J. Numer. Eng. 1994, 37:229-256.
49. Melenk J.M., Babuska I. The partition of unity finite element method: basic theory and applications. Comput. Methods Appl. Mech. Eng. 1996, 139:289-314.
50. Needleman A. A continuum model for void nucleation by inclusion debonding. J. Appl. Mech. - Trans. ASME 1987, 54:525-531.
51. Belytschko T., Lu Y.Y. Element-free Galerkin methods for static and dynamic fracture. Int. J. Solids Struct. 1995, 32:2547-2570.
52. Belytschko T., Lu Y.Y., Gu L. Crack propagation by element-free Galerkin methods. Eng. Fract. Mech. 1995, 51(2):295-9685.
53. Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P. Mesh-less methods: an overview and recent developments. Comput. Methods Appl. Mech. Eng. 1996, 139:3-47.
54. G.N. Wells, Discontinuous Modelling of Strain Localisation and Failure, Ph.D. Thesis, Technische Universiteit Delft, The Netherlands, 2001.
55. Ventura G., Xu J., Belytschko T. A vector level set method and new discontinuity approximation for crack growth by EFG. Int. J. Numer. Methods Eng. 2002, 54(6):923-944.
56. Oliver J., Huespe A.E., Sanchez P.J. A comparative study on finite elements for capturing strong discontinuities: E-fem vs x-fem. Comput. Methods Appl. Mech. Eng. 2006, 195:4732-4752.
57. Zi G., Rabczuk T., Wall W. Extended meshfree methods without branch enrichment for cohesive cracks. Comput. Mech. 2007, 40(2):367-382.
58. Rabczuk T., Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Comput. Mech. 2007, 39(6):743-760.
59. Dolbow J., Belytschko T. An introduction to programming the mesh-less element free Galerkin method. Arch. Comput. Methods Eng. 1998, 5(3):207-241.
60. Rabczuk T., Belytschko T., Xiao S.P. Stable particle methods based on Lagrangian kernels. Comput. Methods Appl. Mech. Eng. 2004, 193:1035-1063.
61. M. Arrea, A.R. Ingraffea, Mixed-mode crack propagation in mortar and concrete, Technical Report 81-13, Department of Structural Engineering, Cornell University, New York, 1982.
62. M.B. Nooru-Mohamed, Mixed-Mode Fracture of Concrete: An Experimental Approach, Ph.D. Thesis, Delft University of Technology, 1992.
63. Ballatore E., Carpinteri A., Ferrara G., Melchiorri G. Mixed mode fracture energy of concrete. Eng. Fract. Mech. 1990, 35:145-157.