Simulation of crack growth using cohesive crack method

Applied Mathematical Modelling

Volumn 34, Issue 9, 2010, Pages 2508-2519

  Zhang, H ^a  

^a WUHAN UNIVERSITY OF TECHNOLOGY   (China)

Author keywords

Concrete; Crack; Fracture; RKPM

Indexed keywords

COHESIVE CRACKS; COHESIVE FORCE; COHESIVE ZONE MODEL; CONCRETE CRACKS; CONCRETE STRUCTURES; CRACK GROWTH; DISCRETE CRACKS; EXPERIMENTAL DATA; MIXED MODE FRACTURE; REPRODUCING KERNEL PARTICLE METHOD; STIFFNESS EQUATIONS; STRAIGHT-LINE SEGMENTS;

FRACTURE; VISIBILITY;

CRACKS;

EID: 77952551030     PISSN: 0307904X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.apm.2009.11.015     Document Type: Article

References (57)

1. Belytschko T., Lu Y.Y. Element-free galerkin methods for static and dynamic fracture. Int. J. Solids Struct. 1995, 32:2547-2570.
2. Belytschko T., Tabbara M. Dynamic fracture using element-free galerkin methods. Int. J. Numer. Method Eng. 1996, 39(6):923-938.
3. Belytschko T., Lu Y.Y., Gu L. Crack propagation by element-free galerkin methods. Eng. Fracture Mech. 1995, 51(2):295-315.
4. Rabczuk T., Zi G. A meshfree method based on the local partition of unity for cohesive cracks. Comput. Mech. 2007, 39(6):743-760.
5. Rabczuk T., Song J.-H., Belytschko T. Simulations of instability in dynamic fracture by the cracking particles method. Eng. Fracture Mech. 2009, 76:730-741.
6. Zi G., Rabczuk T., Wall W.A. Extended meshfree methods without branch enrichment for cohesive cracks. Comput. Mech. 2007, 40(2):367-382.
7. Rabczuk T., Belytschko T. Adaptivity for structured meshfree particle methods in 2D and 3D. Int. J. Numer. Method Eng. 2005, 63(11):1559-1582.
8. Rabczuk T., Xiao S.P., Sauer M. Coupling of meshfree methods with finite elements: basic concepts and test results. Commun. Numer. Meth. Eng. 2006, 22(10):1031-1065.
9. Hao S., Liu W.K., Klein P.A., et al. Modeling and simulation of intersonic crack growth. Int. J. Solids Struct. 2004, 41(7):1773-1799.
10. Cervera M., Oliver J., Herrero E., Oñate E. A computational model for progressive cracking in large dams due to the swelling of concrete. Eng. Fracture Mech. 1990, 35(1-3):573-585.
11. Oliver J., Huespe A.E., Sánchez P.J. A comparative study on finite elements for capturing strong discontinuities: E-FEM vs. X-FEM. Comput. Method Appl. Mech. Eng. 2006, 195(37-40):4732-4752.
12. Rabczuk T., Belytschko T. Application of particle methods to static fracture of reinforced concrete structures. Int. J. Fracture 2006, 137(1-4):19-49.
13. Oliver J., Linero D.L., Huespe A.E., Manzoli O.L. Two-dimensional modeling of material failure in reinforced concrete by means of a continuum strong discontinuity approach. Comput. Method Appl. Mech. Eng. 2008, 197(5):332-348.
14. P.J. Sánchez, A.E. Huespe, J. Oliver, S. Toro, Mesoscopic model to simulate the mechanical behavior of reinforced concrete members affected by corrosion, Int. J. Solids Struct., (2009), in press.
15. T. Rabczuk, T. Belytschko, A three dimensional large deformation meshfree method for arbitrary evolving cracks, Comput. Method Appl. Mech. Eng. 196(29-30) 2777-2799.
16. Rabczuk T., Eibl J. Numerical analysis of prestressed concrete beams using a coupled finite element/element free Galerkin method. Int. J. Solids Struct. 2004, 41(3-4):1061-1080.
17. Rabczuk T., Akkermann J., Eibl J. A numerical model for reinforced concrete structures. Int. J. Solids Struct. 2005, 42(5-6):1327-1354.
18. Rabczuk T., Zi G., Bordas S., Nguyen-Xuan H. A geometrically nonlinear three-dimensional cohesive crack method for reinforced concrete structures. Eng. Fracture Mech. 2008, 75(16):4740-4758.
19. Oller S., Oñate E., Oliver J., Lubliner J. Finite element nonlinear analysis of concrete structures using a " plastic-damage model" Eng. Fracture Mech. 1990, 35(1-3):219-231.
20. Lubliner J., Oliver J., Oller S., Oñate E. A plastic-damage model for concrete. Int. J. Solids Struct. 1989, 25(3):299-326.
21. Faria R., Oliver J., Cervera M. A strain-based plastic viscous-damage model for massive concrete structures. Int. J. Solids Struct. 1998, 35(14):1533-1558.
22. Hao S., Park H.S., Liu W.K. Moving particle finite element method. Int. J. Numer. Method Eng. 2002, 53(8):1937-1958.
23. Hao S., Liu W.K. Moving particle finite element method with superconvergence: Nodal integration formulation and applications. Comput. Method Appl. Mech. Eng. 2006, 195(44-47):6059-6072.
24. Hao S., Liu W.K., Chang C.T. Computer implementation of damage models by finite element and meshfree methods. Comput. Method Appl. Mech. Eng. 2000, 187(3-4):401-440.
25. Liu W.K., Hao S., Belytschko T., Li S.F., Chang C.T. Multiple scale meshfree methods for damage fracture and localization. Comput. Mater. Sci. 1999, 16(1-4):197-205.
26. Cervera M., Faria R., Oliver J., Prato T. Numerical modelling of concrete curing, regarding hydration and temperature phenomena. Comput. Struct. 2002, 80(18-19):1511-1521.
27. Hao S., Liu W.K., Weertman J. Cohesive solutions of intersonic moving dislocations. Philos. Mag. 2004, 84(11):1067-1104.
28. 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. Method Eng. 2008, 75:577-599.
29. Rabczuk T., Areias P.M.A., Belytschko T. A simplified meshfree method for shear bands with cohesive surfaces. Int. J. Numer. Method Eng. 2007, 69(5):993-1021.
30. Rabczuk T., Areias P.M.A., Belytschko T. A meshfree thin shell method for non-linear dynamic fracture. Int. J. Numer. Method Eng. 2007, 72(5):524-548.
31. Rabczuk T., Areias P.M.A. A meshfree thin shell for arbitrary evolving cracks based on an external enrichment. Comput. Model. Eng. Sci. 2008, 16(2):115-130.
32. Oliver J., Huespe A.E., Pulido M.D.G., Chaves E. From continuum mechanics to fracture mechanics: the strong discontinuity approach. Eng. Fracture Mech. 2002, 69(2):113-136.
33. Oliver J., Huespe A.E. Continuum approach to material failure in strong discontinuity settings. Comput. Method. Appl. Mech. Eng. 2004, 193(30-32):3195-3220.
34. Bazant Z.P., Belytschko T. Wave propagation in a strain softening bar: exact solution. J. Eng. Mech. ASCE 1985, 11:381-389.
35. Barenblatt G. The mathematical theory of equilibrium of cracks in brittle fracture. Adv. Appl. Fracture 1962, 7:55-129.
36. 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.
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. Fracture Mech. 2008, 75(5):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., Samaniego E. Discontinuous modelling of shear bands with adaptive meshfree methods. Comput. Method Appl. Mech. Eng. 2008, 197(6-8):641-658.
40. Nguyen V.P., Rabczuk T., Bordas S., Duflot M. Meshless methods: a review and computer implementation aspects. Math. Comput. Simulat. 2008, 79:763-813.
41. Belytschko T., Lu Y.Y., Gu L. Element-free galerkin methods. Int. J. Numer. Method Eng. 1994, 37:229-256.
42. Ventura G., Xu J., Belytschko T. A vector level set method and new discontinuity approximation for crack growth by efg. Int. J. Numer. Method Eng. 2002, 54(6):923-944.
43. Liu W.K., Jun S., Zhang Y.F. Reproducing kernel particle methods. Int. J. Numer. Method Fluid 1995, 20:1081-1106.
44. Lucy L. A numerical approach to the testing of the fission hypothesis. Astron. J. 1977, 82:1013-1024.
45. Beissel S., Belytschko T. Nodal integration of the element-free galerkin method. Comput. Method Appl. Mech. Eng. 1996, 139:49-74.
46. Belytschko T., Krongauz Y., Organ D., Fleming M., Krysl P. Meshless methods: an overview and recent developments. Comput. Method Appl. Mech. Eng. 1996, 139:3-47.
47. Bonet J., Kulasegaram S. Correction and stabilization of smooth particle hydrodynamics methods with application in metal forming simulations. Int. J. Numer. Method Eng. 2000, 47(6):1189-1214.
48. Dilts G.A. Moving least square particle hydrodynamics i: consistency and stability. Int. J. Numer. Method Eng. 2000, 44:1115-1155.
49. Krongauz Y., Belytschko T. Consistent pseudo derivatives in mesh-20 less methods. Comput. Method Appl. Mech. Eng. 1997, 146:371-386.
50. Rabczuk T., Belytschko T., Xiao S.P. Stable particle methods based on lagrangian kernels. Comput. Method Appl. Mech. Eng. 2004, 193:1035-1063.
51. Rabczuk T., Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. Int. J. Numer. Method Eng. 2004, 61(13):2316-2343.
52. Belytschko T., Chend H., Xu J., Zi G. Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. Int. J. Numer. Method Eng. 2003, 58(12):1873-1905.
53. Xu X.-P., Needleman A. Numerical simulations of fast crack growth in brittle solids. J. Mech. Phys. Solid 1994, 42:1397-1434.
54. M.B. Nooru-Mohamed, Mixed-mode fracture of concrete: an experimental approach, Ph.D. thesis, Delft University of Technology, 1992.
55. Alfaiate J., Pires Eb, Martins J.A.C. A finite element analysis of nonprescribed crack propagation in concrete. Comput. Struct. 1997, 63:17-26.
56. Prasad M.V.K.V., Krishnamoorthy C.S. Computational model for discrete crack growth in plain and reinforced concrete. Comput. Method Appl. Mech. Eng. 2002, 191:2699-2725.
57. 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.