Three-Dimensional Modeling of Concrete Structures. I: Plain Concrete
Publication: Journal of Structural Engineering
Volume 123, Issue 10
Abstract
A triaxial constitutive model for finite-element (FE) analysis of preand postcracking behavior of concrete is presented. A five-parameter ultimate strength envelope is used in the stress space. For compression dominated loading leading to crushing, a modified version of a conceptually simple hypoelastic model is used and augmented to capture the postcrushing strain softening behavior approximately. Various test data on multiaxial loading of concrete are analyzed to verify the capabilities of the model. The postcracking strain softening formulation is based on the fracture energy concept with multiple nonorthogonal crack capability. To maintain the objectivity with respect to mesh refinement, a simple method is proposed to compute the crack band widths within 20-noded solid isoparametric elements. This model is verified by analyzing the postcracking response of a uniaxial tensile member, a test notched beam, and a beam subjected to torsion.
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References
1.
Balmer, G. G. (1949). “Shearing strength of concrete under high triaxial stress-computation of Mohr's envelope as a curve.”Bur. Reclam. Struct. Res. Lab., Rep. SP-23.
2.
Barzegar, F., and Maddipudi, S.(1994). “Generating reinforcement in FE modeling of concrete structures.”J. Struct. Engrg., ASCE, 120(5), 1656–1662.
3.
Barzegar, F., and Maddipudi, S.(1997). “Three-dimensional modeling of concrete structures. II: Reinforced concrete.”J. Struct. Engrg., ASCE, 123(10), 1347–1356.
4.
Bažant, Z. P., and Cedolin, L.(1979). “Blunt crack band propagation in finite element analysis.”J. Engrg. Mech. Div., ASCE, 105(2), 297–315.
5.
Bažant, Z. P., and Oh, B. H.(1983). “Crack band theory for fracture of concrete.”Mat. and Struct., 16(94), 155–177.
6.
Bažant, Z. P., and Pijaudier-Cabot, G.(1989). “Measurement of characteristic length of nonlocal continuum.”J. Engrg. Mech., ASCE, 115(4), 755–767.
7.
Bongers, J. P. W., Rutten, H. S., Van Mier, J. G. M., and Fijneman, H. J. (1994). “Softening behavior of concrete loaded in multiaxial compression.”Computer modeling of concrete structures; Proc., Euro-C 1994 Int. Conf., Vol. 1, 303–312.
8.
Cedolin, L., Crutzen, Y. R. J., and Dei Poli, S.(1977). “Triaxial stress-strain relationship for concrete.”J. Engrg. Mech. Div., ASCE, 103(3), 423–439.
9.
Cervera, M. (1986). “Nonlinear analysis of reinforced concrete structures using three dimensional and shell finite element models,” PhD dissertation, Dept. of Civ. Engrg., Univ. Coll. of Swansea, Wales.
10.
Channakeshava, C. (1987). “Elasto-plastic-cracking analysis of plain and reinforced concrete structures,” PhD dissertation, Indian Inst. of Sci., Bangalore, India.
11.
De Borst, R., and Nauta, P.(1985). “Non-orthogonal cracks in a smeared finite element model.”Engrg. Computations, 2(3), 35–46.
12.
Eberhardsteiner, J., Meschke, G., and Mang, H. A. (1987). “Comparison of constitutive models for triaxially loaded concrete.”Computational Mech. of Concrete Struct.—Adv. and Applications, IABSE Colloquium, Delft, The Netherlands, 197–208.
13.
Feenstra, P. H., and De Borst, R. (1993). “Aspects of robust computational modeling for plain and reinforced concrete.”Heron, 38(4).
14.
“Finite element analysis of reinforced concrete.” (1982). State of the Art Rep., Task Com. on Concrete and Masonry Struct., ASCE, New York, N.Y.
15.
“Finite element analysis of reinforced concrete structures II.” (1993). Proc., the Int. Workshop, ASCE, New York, N.Y.
16.
Gerstle, K. H.(1981a). “Simple formulation of biaxial concrete behavior.”ACI J., 78(1), 62–68.
17.
Gerstle, K. H.(1981b). “Simple formulation of triaxial concrete behavior.”ACI J., 78(5), 382–387.
18.
Irons, B. M.(1971). “Quadrature rules for brick based finite elements.”Int. J. Numer. Methods in Engrg., 3(2), 293–294.
19.
Karihaloo, B. L., and Nallathambi, P. (1991). “Notched beam test: mode I fracture toughness.”Fracture mechanics test methods for concrete, S. P. Shah and A. Carpinteri, eds., Chapman & Hall, Ltd., London, England, 1–86.
20.
Kotsovos, M. D., and Newman, J. B.(1978). “Generalized stress-strain relations for concrete.”J. Engrg. Mech. Div., ASCE, 104(4), 845–856.
21.
Kotsovos, M. D., and Newman, J. B.(1979). “A mathematical description of the deformational behavior of concrete under complex loading.”Mag. Concrete Res., 31(107), 77–90.
22.
Kupfer, H., Hilsdorf, H. K., and Rüsch, H.(1969). “Behavior of concrete under biaxial stresses.”ACI J., 66(8), 656–666.
23.
Launay, P., and Gachon, H. (1972). “Strain and ultimate strength of concrete under triaxial stress.”ACI SP-34, Am. Concrete Inst., Paper 13, American Concrete Institute (ACI), Detroit, Mich.
24.
Maddipudi, S. (1992). “Three dimensional nonlinear analysis of components of reinforced concrete framed structures,” PhD dissertation, Dept. of Civ. Engrg., Louisiana State Univ., La.
25.
Malvar, L. J., and Fourney, M. E. (1990). “A three dimensional application of the smeared crack approach.”Engrg. Fracture Mech., 35(1/2/3), 251–260.
26.
Oliver, J.(1989). “A consistent characteristics length for smeared cracking model.”Int. J. Numer. Methods in Engrg., 28, 461–474.
27.
RILEM Draft Recommendation (50-FMC).(1985). “Determination of the fracture energy of mortar and concrete by means of three-point bend tests on notched beams.”Mat. and Struct., 18, 287–290.
28.
Rots, J. G. (1988). “Computational modeling of concrete fracture,” Dissertation, Dept. of Civ. Engrg., Delft Univ. of Technol., The Netherlands.
29.
Rots, J. G., Nauta, P., Kusters, G. M. A., and Blaauwendraad, J. (1985). “Smeared crack approach and fracture localization in concrete.”Heron, 30(1).
30.
Scavuzzo, R. (1982). “Behavior of concrete under multiaxial load histories,” MS thesis, Dept. of Civ., Envir., and Arch. Engrg., Univ. of Colorado, Boulder, Colo.
31.
Scavuzzo, R., Cornelius, V. H., Gerstle, K. H., Ko, H. Y., and Stankowski, T. (1983). “Simple formulation of concrete response to multiaxial load cycles.”Proc., Int. Conf. on Constitutive Relations, Univ. of Arizona, Tucson, Ariz., 421–426.
32.
Scott, B. D., Park, R., and Priestly, M. J. N.(1982). “Stress-strain behavior of concrete confined by overlapping hoops at low and high strain rates.”ACI J., 79, 13–27.
33.
Selby, R. G., and Vecchio, F. J. (1993). “Three-dimensional constitutive relations for reinforced concrete.”Publ. No. 93-02, Dept. of Civ. Engrg., Univ. of Toronto, Canada.
34.
Stankowski, T. (1983). “Concrete under multiaxial load histories,” MS thesis, Dept. of Civ., Envir., and Arch. Engrg., Univ. of Colorado, Boulder, Colo.
35.
Stankowski, T., and Gerstle, K. H.(1985). “Simple formulation of concrete behavior under multiaxial load histories.”ACI J., 82(2), 213–221.
36.
Vonk, R. A. (1993). “A micromechanical investigation of softening of concrete loaded in compression.”Heron, 38(3).
37.
Willam, K. J., and Waranke, E. P.(1975). “Constitutive model for the triaxial behavior of concrete.”Int. Assn. for Bridge and Struct. Engrg., 19, 1–30.
Information & Authors
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Published In
Journal of Structural Engineering
Volume 123 • Issue 10 • October 1997
Pages: 1339 - 1346
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Oct 1, 1997
Published in print: Oct 1997
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