Energy-Based Cohesive Crack Propagation Modeling
Publication: Journal of Engineering Mechanics
Volume 121, Issue 12
Abstract
This paper presents an energy-based approach for the finite-element modeling of mixed-mode cohesive crack propagation. This approach predicts the propagation of a quasistatic cohesive crack based on the principle of energy conservation. The crack propagation direction is assumed to be perpendicular to the direction of the maximum tensile principal stress at the cohesive crack tip. A generalized virtual crack-extension technique including the cohesive crack model is used to efficiently evaluate the crack propagation condition. The energy-based approach is both theoretically more fundamental and numerically more accurate than the commonly used strength-based cohesive crack modeling approach. A two-dimensional automatic mixed-mode discrete crack propagation modeling program has been developed that is capable of modeling both nonlinear and linear elastic crack propagation problems. The numerical efficiency and convergence behavior of the present approach are demonstrated through two example problems: a three-point bend beam and a single edge-notched shear beam.
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References
1.
Arrea, A., and Ingraffea, A. R. (1982). “Mixed-mode crack propagation in mortar and concrete.”Rep. No. 81-13, Dept. of Struct. Engrg., Cornell Univ., Ithaca, N.Y.
2.
Ayari, M. L., and Saouma, V. E. (1990). “A fracture mechanics based seismic analysis of concrete gravity dams using discrete cracks.”Engrg. Fracture Mech., 35(1/2/3), 587–598.
3.
Bažant, Z. P.(1986). “Mechanics of distributed cracking.”Appl. Mech. Rev., 39(5), 675–705.
4.
Bažant, Z. P.(1994). “Nonlocal damage theory based on micromechanics of crack interactions.”J. Engrg Mech., ASCE, 120(3), 593–617.
5.
Bažant, Z. P., and Li, Y. N. (1994). “Cohesive crack model for geomaterials: stability analysis and rate effect.”Appl. Mech. Rev., 47(6), S91–S96.
6.
Bažant, Z. P., and Lin, F. B.(1988). “Nonlocal smeared cracking model for concrete fracture.”J. Struct. Engrg., ASCE, 114(11), 2493–2510.
7.
Bažant, Z. P., and Oh, B. H.(1983). “Crack band theory for fracture of concrete.”Mat. and Struct., Paris, France, 16(93), 155–177.
8.
Bažant, Z. P., and Pijaudier-Cabot, G.(1989). “Measurement of characteristic length of nonlocal continuum.”J. Engrg. Mech., 115(4), 755–767.
9.
Bocca, P., Carpinteri, A., and Valente, S.(1991). “Mixed mode fracture of concrete.”Int. J. Solids and Struct., 27(9), 1139–1153.
10.
Bolander, J., and Hiroshi, H. (1992). “Applying nonlocal smeared crack concepts to modeling concrete fracture.”Proc., 1st Int. Conf. on Fracture Mech. of Concrete Struct., Z. P. Bažant, ed., Elsevier Science Publishers Ltd., New York, N.Y., 227–238.
11.
Broek, D. (1987). Elementary engineering fracture mechanics . Martinus Nijhoff Publishers, Dordrecht, The Netherlands.
12.
Chappel, J. F., and Ingraffea, A. R. (1981). “A fracture mechanics investigation of the cracking of Fontana Dam.”Rep. No. 81-7, Dept. of Struct. Engrg., Cornell Univ., N.Y.
13.
Chen, Z., and Schreyer, H. L. (1991). “Secant structural solution strategies under element constraint for incremental damage.”Comp. Methods in Appl. Mech. and Engrg., 90(1-3), 869–884.
14.
de Borst, R., Muhlhaus, H. B., and Pamin, J. (1992). “A gradient continuum model for Mode-I fracture in concrete and rock.”Proc., 1st Int. Conf. on Fracture Mech. of Concrete Struct., Z. P. Bažant, ed., Elsevier Science Publishers Ltd., New York, N.Y., 227–238.
15.
Erdogan, F., and Sih, G. C.(1963). “On the crack extension in plate under in plane loading and transverse shear.”J. Basic Engrg., 85(4), 519–527.
16.
Gerstle, W. H., and Abdalla, J. E. (1990). “Finite element meshing criteria for crack problems.”ASTM STP 1074, ASTM, Philadelphia, Pa., 509–521.
17.
Gerstle, W. H., and Xie, M.(1992). “FEM modeling of fictitious crack propagation in concrete.”J. Engrg. Mech., ASCE, 118(2), 416–434.
18.
Griffith, A. A. (1921). “The phenomena of rupture and flow in solids.”Phil. Trans. Roy. Soc. London, Series A, London, U.K.; 221, 163–197.
19.
Gustafsson, P. J. (1985). “Fracture mechanics studies of non-yielding materials like concrete.”Rep. TVBM-1007, Div. of Build. Mat., Lund Inst. of Tech., Lund, Sweden.
20.
Haber, R. B., and Koh, H. M.(1985). “Explicit expressions for energy release rates using virtual crack extensions.”Int. J. Numerical Methods in Engrg., 21(2), 301–315.
21.
Hellen, T. K.(1975). “On the method of virtual crack extensions.”Int. J. Numerical Methods in Engrg., 9(1), 187–207.
22.
Hellen, T. K.(1989). “Virtual crack extension methods for non-linear materials.”Int. J. Numerical Methods in Engrg., 28(4), 929–942.
23.
Hillerborg, A., Modeer, M., and Petersson, P. E.(1976). “Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements.”Cement and Concrete Res., 6(6), 773–782.
24.
Horri, H., and Ichinomiya, T.(1991). “Observation of fracture process zone by laser speckle technique and governing mechanism in fracture of concrete.”Int. J. Fracture, 51(1), 19–29.
25.
Huerta, A., and Pijaudier-Cabot, G.(1994). “Discretization influence on regularization by two localization limiters.”J. Engrg. Mech., 120(6), 1198–1218.
26.
Hussain, M. A., Pu, S. L., and Underwood, J. H. (1974). “Strain energy release rate for a crack under combined mode I and mode II.”Fracture Anal., ASTM STP 560, ASTM, Philadelphia, Pa.
27.
Ingraffea, A. R. (1989). “Shear cracks.”Fracture mechanics of concrete structures, L. Elfgren, ed., Chapman and Hall, London, U.K., 231–232.
28.
Ingraffea, A. R., and Gerstle, W. H. (1984). “Nonlinear fracture models for discrete crack propagation.”Proc., NATO Adv. Workshop on Application of Fracture Mech. to Cementitious Composites, S. P. Shah, ed., M. Nijhoff, Hingham, Mass.
29.
Ingraffea, A. R., Gerstle, W. H., Gergely, P., and Saouma, V.(1984). “Fracture mechanics of bond in reinforced concrete.”J. Struct. Engrg., ASCE, 110(4), 871–890.
30.
Ingraffea, A. R., and Panthaki, M. (1985). “Analysis of `shear fracture' tests of concrete beams.”Proc., Japan-U.S. Joint Seminar on Finite Element Anal. of Reinforced Concrete, C. Meyer and H. Okamura, eds., ASCE, New York, N.Y., 151–173.
31.
Ingraffea, A. R., and Saouma, V. (1985). “Numerical modeling of discrete crack propagation in reinforced and plain concrete.”Fracture mechanics of concrete: Structural application and numerical calculation, G. Sih and A. DiTommaso, eds., Martinus Nijhoff Publishers, Dordrecht, The Netherlands, 171–225.
32.
Li, Y. N., and Liang, R. Y.(1992). “Stability theory of cohesive crack model.”J. Engrg. Mech., ASCE, 118(3), 587–603.
33.
Li, Y. N., and Liang, R. Y.(1994). “Peak load determination in linear fictitious crack model.”J. Engrg. Mech., ASCE, 120(2), 232–249.
34.
Muhlhaus, H.-B., and Vardoulakis, I.(1987). “The thickness of shear bands in granular materials.”Géotechnique, London, U.K., 37(3), 271–283.
35.
Olmsted, J. H. (1966). Calculus with analytic geometry . Meredith Publishing Co., New York, N.Y.
36.
Pan, Y. C., Marchertas, A. H., Pfeiffer, P. A., and Kennedy, J. M.(1984). “Concrete cracking simulations for nuclear applications.”Theoretical Appl. Fracture Mech., 2(1), 27–38.
37.
Parks, D. M.(1974). “A stiffness derivative finite element technique for determination of crack tip stress intensity factors.”Int. J. Fracture, 10(4), 487–502.
38.
Parks, D. M.(1977). “The virtual crack extension method for nonlinear material behavior.”Comp. Methods in Appl. Mech. and Engrg., 12(3), 353–364.
39.
Petersson, P. E. (1981). “Crack growth and development of fracture zone in plain concrete and similar materials.”Rep. TVBM-1006, Div. of Build. Mat., Lund Inst. of Tech., Lund, Sweden.
40.
Rots, J. G.(1991). “Smeared and discrete representations of localized fracture.”Int. J. Fracture, 51(1), 45–59.
41.
Rots, J. G., and de Borst, R.(1987). “Analysis of mixed-mode fracture in concrete.”J. Engrg. Mech., ASCE, 113(11), 1739–1758.
42.
Sha, G. T. (1984). “On the virtual crack extension technique for stress intensity factors and energy release rate calculations for mixed fracture mode.”Int. J. Fracture, 25(2), R33–R42.
43.
Sih, G. C.(1974). “Strain-energy-density factor applied to mixed-mode crack problems.”Int. J. Fracture, 10(3), 305–321.
44.
Sussman, T., and Bathe, K. J.(1985). “The gradient of the finite element variational indicator with respect to nodal polar coordinates.”Int. J. Numerical Methods in Engrg., 21(4), 763–774.
45.
Swenson, D., and Ingraffea, A. R.(1991). “The collapse of the Schoharie Creek Bridge: a case study in concrete fracture mechanics.”Int. J. Fracture, 51(1), 73–92.
46.
Underwood, P. (1983). “Dynamic relaxation.”Computational methods in mechanics for transient analysis, T. Belytschko and T. J. R. Hughes, eds., North-Holland Publishing, Amsterdam, The Netherlands, 245–265.
47.
Wawrzynek, P. A. (1986). “Interactive finite element analysis of fracture processes: an integrated approach.” MS thesis, Dept. of Struct. Engrg., Cornell Univ., Ithaca, N.Y.
48.
Xie, M., Gerstle, W. H., and Chen, Z. (1994). “Finite element analysis of combined smeared and discrete mechanisms in rock salt.”Proc., 8th Int. Conf. of the Int. Assoc. for Comp. Methods and Adv. in Geomech., Siriwardane and Zaman, eds., Elsevier Science Publishers Ltd., New York, N.Y.
49.
Xie, M., Gerstle, W. H., and Rahulkumar, P.(1995). “Energy-based automatic mixed-mode crack propagation modeling.”J. Engrg. Mech., ASCE, 121(8), 914–923.
50.
Zhou, F. P. (1992). “Time-dependent crack growth and fracture in concrete,” PhD thesis, Rep. TVBM-1011, Div. of Build. Mat., Lund Inst. of Tech., Lund, Sweden.
51.
Zienkiewicz, O. C., and Taylor, R. L. (1989). The finite element method . McGraw-Hill Book Co., London, U.K.
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Information
Published In
Journal of Engineering Mechanics
Volume 121 • Issue 12 • December 1995
Pages: 1349 - 1358
Copyright
Copyright © 1995 American Society of Civil Engineers.
History
Published online: Dec 1, 1995
Published in print: Dec 1995
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