FEM Modeling of Fictitious Crack Propagation in Concrete
Publication: Journal of Engineering Mechanics
Volume 118, Issue 2
Abstract
Using a mixed‐mode extension of the Hillerborg fictitious crack model, a practical interface finite element approach is used to model discrete crack propagation. The fictitious crack tip propagates perpendicular to the maximum tensile principal stress at its tip when the tensile strength is exceeded. A dynamic relaxation method is employed. Interface elements have been used before to model such cracks; however, the software technology is in a state of rapid development, making possible improvements in the modeling of discrete nonlinear crack propagation. The concept of fracture process zone is broadened to one of interface process zone, which includes the nonlinear behavior of the fracture process zone as well as the crack face interference behind the fracture process zone. A development makes the method efficient while preserving the accuracy of the fictitious crack model. The fictitious crack is represented by interface elements with linearly varying displacements; however, the traction distribution is arbitrary. As example problems demonstrate, these assumptions allow the fictitious crack to be modeled using few degrees of freedom without compromising accuracy. Modeling of the size effect is presented.
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References
1.
Arrea, M., and Ingraffea, A. R. (1982). “Mixed‐mode crack propagation in mortar and concrete.” Report No. 81‐113, Cornell Univ., Ithaca, N.Y.
2.
Ballatore, E., Carpinteri, A., Ferrara, G., and Melchiorri, G. (1990). “Mixed mode fracture energy of concrete.” Engrg. Fract. Mech., 35(1/2/3), 145–157.
3.
Bazant, Z. P., and Cedolin, L. (1979). “Blunt crack band propagation in finite element analysis.” J. Engrg. Mech. Div., ASCE, 105(2), 297–315.
4.
Bazant, Z. P. (1987). “Fracture energy of heterogeneous materials and similitude.” SEM/RILEM Int. Conf. on Fracture of Concrete and Rock, S. P. Shah, and S. E. Swartz, eds., Society for Experimental Mechanics, Bethel, Conn.
5.
Bocca, P., Carpinteri, A., and Valente, S. (1991). “Mixed mode fracture of concrete.” Int. J. Solids Struct., 27(9), 1139–1153.
6.
Castro‐Montero, A., Shah, S. P., and Miller, R. A. (1990). “Strain field measurement in fracture process zone.” J. Engrg. Mech., ASCE, 116(11), 2463–2484.
7.
de Borst, R. (1986). “Nonlinear analysis of frictional materials,” thesis presented to Delft Univ. of Tech., at Delft, the Netherlands, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
8.
Desai, C. S., Zaman, M. M., Lightner, J. G., and Siriwardane, H. J. (1984). “Thinlayer element for interfaces and joints.” Int. J. Numer. Anal. Methods Geotech., 8, 19–43.
9.
Elfgren, L. (1989). Fracture mechanics of concrete structure. Chapman and Hall, London, U.K.
10.
Goodman, R. E., Taylor, R. L., and Brekke, T. L. (1968). “A model for the mechanics of jointed rock.” J. Soil Mech. and Found. Div., ASCE, 94(3), 637–659.
11.
Gustafsson, P. J. (1985). “Fracture mechanics studies of non‐yielding materials like concrete.” Report TVBM‐1007, Lund Inst. of Tech., Lund, Sweden.
12.
Heuze, F. E., and Barbour, T. G. (1982). “New models for rock joints and interfaces.” J. Geotech. Engrg. Div., ASCE, 108(5), 757–776.
13.
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.” Cem. Concr. Res., 6(6), 773–782.
14.
Hillerborg, A. (1985). “A comparison between the size effect law and the fictitious crack model.” Dei Poli anniversary volume, L. Cedolin, ed., Politecnico di Milano, Milan, Italy, 331–334, 335–338.
15.
Hillerborg, A., and Rots, J. (1989). “Crack opening and numerical modelling.” Fracture Mechanics of Concrete Structures, L. Elfgren, ed., Chapman and Hall, London, U.K., 128–146.
16.
Ingraffea, A. R., and Gerstle, W. H. (1984). “Nonlinear fracture models for discrete crack propagation.” Proc. NATO Advanced Workshop on Application of Fracture Mechanics to Cementitious Composites, S. P. Shah, ed., M. Nijhoff, Hingham, Mass.
17.
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.
18.
Ingraffea, A. R., and Saouma, V. (1984). “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, Hingham, Mass., 171–225.
19.
Jenq, Y. S., and Shah, S. P. (1985a). “A fracture toughness criterion for concrete.” Engrg. Fract. Mech., 21(5), 1055–1069.
20.
Jenq, Y. S., and Shah, S. P. (1985b). “Two parameter fracture model for concrete.” J. Engrg. Mech., ASCE, 111(10) 1227–1241.
21.
Jenq, Y. S., and Shah, S. P. (1987). “Mixed mode fracture parameters of concrete.” SEM/RILEM Int. Conf. on Fracture of Concrete and Rock, S. P. Shah, and S. E. Swartz, eds., Society for Experimental Mechanics, Bethel, Conn., 359–369.
22.
Kaplan, M. F. (1961). “Crack propagation and the fracture of concrete.” J. Am. Concr. Inst., 58(5), 591–610.
23.
Kesler, C., Naus, D., and Lott, J. (1972). “Fracture mechanics—Its applicability to concrete.” Proc. 1971 Int. Conf. on Mechanical Behavior of Materials, Vol. IV, 113–124.
24.
Papadrakakis, M. (1981). “A method for the automatic evaluation of the dynamic relaxation parameters.” Comput. Methods Appl. Mech. Engrg., 25(1), 35–48.
25.
Petersson, P. E. (1981). “Crack growth and development of fracture zone in plain concrete and similar materials.” Report TVBM‐1006, Lund Inst. of Tech., Lund, Sweden.
26.
Roberson, J. A., and Crowe, C. T. (1975). Engineering fluid mechanics. Houghton Mifflin Co., Boston, Mass.
27.
Rots, J. G., and deBorst, R. (1987). “Analysis of mixed‐mode fracture in concrete.” J. Engrg. Mech., ASCE, 113(11), 1739–1758.
28.
Stone, C. S., Krieg, R. D., and Beisinger, Z. E. (1985). “SANCHO A finite element computer program for the quasistatic, large deformation, inelastice response of two‐dimensional solids.” Report, SAND84‐2618, Sandia National Lab., Albuquerque, N.M.
29.
Swartz, S. E., and Taha, N. M. (1990). “Mixed mode crack propagation and fracture in concrete.” Engrg. Fract. Mech., 35(1/2/3), 137–144.
30.
Swenson, D. V., and Ingraffea, A. R. (1988). “Modelingmixed‐mode dynamic crack propagation using finite elements: Theory and applications, 3.” Comput. Mech., 3, 381–397.
31.
Swenson, D., and Chih‐Chien, C. (1990). “Development of computer program to analyze fracture in layered structures.” Report 223, Kansas State Univ., Manhattan, Kans.
32.
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.
33.
Xie, M., Gerstle, W. H., and Panthaki, M. (1990). “Fracture analysis of cementitious seals for nuclear waste isolation.” Fracture behavior and design of materials and structures, Proc. of the Eighth Biennial European Conf. on Fracture, D. Firrao, ed., Engineering Materials Advisor Services, Ltd., Warley, West Midlands, U.K., 786–791.
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Published In
Journal of Engineering Mechanics
Volume 118 • Issue 2 • February 1992
Pages: 416 - 434
Copyright
Copyright © 1992 ASCE.
History
Published online: Feb 1, 1992
Published in print: Feb 1992
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