Hypoelastic Tridimensional Model for Nonproportional Loading of Plain Concrete
Publication: Journal of Engineering Mechanics
Volume 123, Issue 11
Abstract
A generalized constitutive model based on hypoelastic theory is proposed to characterize the stress-strain relationship of plain concrete under monotonic and cyclic nonproportional loading. First, the existing hypoelastic incremental models are reviewed and some features of concrete behavior are described. The behavior of concrete is modeled using a normalized scalar damage parameter, the equivalent strain concept, and either the Willam-Warnke five-parameter or the Hsieh-Ting-Chen four-parameter failure surfaces. A new tensile strength criterion and a method for objective modeling of the postpeak compression state are derived. The important features of nonlinear behavior of concrete, such as the volumetric dilatation, the transition state from brittle-softening to ductile-hardening behavior, degradation of the elastic modulus under cyclic loading, and the postcrushing state are all represented by the proposed constitutive model. Comparison of the model predictions with laboratory tests support the validity of the proposed formulation. It is believed that the proposed constitutive relationships provide a good compromise between simplicity and accuracy for modeling plain concrete.
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References
1.
Balakrishnan, S., and Murray, D.(1988). “Concrete constitutive model for NLFE analysis of structures.”J. Struct. Engrg., ASCE, 114(7), 1449–1466.
2.
Bažant, Z. P.(1983). “Comment on orthotropic models for concrete and geomaterials.”J. Engrg. Mech., ASCE, 109(3), 849–865.
3.
Bažant, Z. P., and Oh, B. H.(1983). “Crack band theory for fracture of concrete.”Mat. and Struct., 16, 155–177.
4.
Bouzaiene, A. (1995). “Caractérisation et modélisation du comportement non linéaire d'éléments en béton non armé et armé sous sollicitations multiaxiales,” PhD dissertation, École Polytechnique de Montréal, Québec, Canada (in French).
5.
Chen, E. S., and Buyukozturk, O.(1985). “Constitutive model for concrete in cyclic compression.”J. Engrg. Mech., ASCE, 111(6), 797–814.
6.
Crisfield, M. A., and Wills, J.(1989). “Analysis of R/C panels using different concrete models.”J. Engrg. Mech., ASCE, 115(3), 578–597.
7.
Darwin, D., and Pecknold, D. A.(1976). “Analysis of R/C shear panels under cyclic loading.”J. Struct. Div., ASCE, 102(2), 355–369.
8.
Darwin, D., and Pecknold, D. A.(1977). “Nonlinear biaxial stress-strain law for concrete.”J. Engrg. Mech. Div., ASCE, 103(2), 229–241.
9.
Elwi, A. E., and Murray, D. W.(1979). “A 3D hypoelastic concrete constitutive relationship.”J. Engrg. Mech. Div., ASCE, 105(4), 623–641.
10.
Han, D. J., and Chen, W. F. (1985). “A nonuniform hardening plasticity model for concrete materials.”Mech. of Mat., 4(3, 4), 283–302.
11.
Hasegawa, T., and Bažant, Z. P.(1993). “Nonlocal microplane concrete model with rate effect and load cycles. I: General formulation.”J. Mat. in Civ. Engrg., ASCE, 5(3), 372–393.
12.
Hillerborg, A. (1989). “Size dependency of the stress-strain curve in compression.”Analysis of concrete structures by fracture mechanics, Elfgren and Shah, eds., RILEM, Proceeding 6, 171–178.
13.
Hsieh, S. S., Ting, E. C., and Chen, W. F.(1982). “A plasticity-fracture model for concrete.”Int. J. of Solids Struct., 18(3), 181–197.
14.
Hsu, T. T. C., Slate, F. O., Sturman, G. M., and Winter, G.(1963). “Microcracking of plain concrete and the shape of the stress-strain curve.”Am. Concrete Inst. J., 60(2), 209–223.
15.
Kostovos, M. D.(1979). “Fracture processes of concrete under generalized stress states.”Mat. and Struct., 12(72), 431–437.
16.
Kostovos, M. D.(1983). “Effect of testing techniques on the post-ultimate behavior of concrete in compression.”Mat. and Struct., 16(91), 3–12.
17.
Kupfer, H. B., Hillsdorf, H. K., and Rusch, H.(1969). “Behavior of concrete under biaxial stress.”Am. Concrete Inst. J., 66(8), 656–666.
18.
Maekawa, K., and Okamura, H. (1983). “The deformational behavior and constitutive equation of concrete, using the elasto-plastic and fracturing model.”J. Facu. of Engrg., University of Tokyo, Japan, XXXVII(2), 253–328.
19.
Massicotte, B., Elwi, A. E., and MacGregor, J. G. (1988). “Analysis of reinforced concrete panels loaded axially and transversely.”Struct. Engrg. Rep. No. 161, Dept. of Civ. Engrg., Univ of Alberta, Edmonton, Canada.
20.
Mazars, J. (1984). “Applications de la mécanique de l'endommagement au comportement non linéaire et à la rupture du béton de structure,” Thèse d'Etat, Université Paris VI, France.
21.
Morita, S., and Kaku, T. (1975). “Force-strain relationship of reinforcing bars embedded in concrete under reserved loading.”Bulletin d'Information, (132), CEB, Switzerland.
22.
Oliver, J.(1989). “A consistent characteristic length of smeared cracking models.”Int. J. Numer. Methods in Engrg., 28, 461–474.
23.
Pagoni, S. J., Moussa, A., and Buyukozturk, O.(1992). “A nonlinear three-dimensional analysis of reinforced concrete based on bounding surface model.”Comp. and Struct., 43(1), 1–12.
24.
Palaniswamy, R., and Shah, S.(1974). “Fracture and stress-strain relationship of concrete under triaxial compression.”J. Struct. Engrg. Div., ASCE, 100(5), 901–916.
25.
Pramono, E., and Willam, K. J.(1989). “Fracture energy-based plasticity formulation of plain concrete.”J. Engrg. Mech., ASCE, 115(6), 1183–1204.
26.
Read, H. E., and Hegemier, G. A. (1984). “Strain-softening of rock, soil and concrete—a review article.”Mech. of Mat., (3), 271–294.
27.
Rots, J. G. (1988). “Computational modeling of concrete fracture,” PhD dissertation, Delft Univ. of Technol., Delft, The Netherlands.
28.
Saenz, L. P.(1964). “Discussion of equation for stress-strain curve of concrete—by Desai and Krishnan.”Am. Concrete Inst., 61(9), 1229–1235.
29.
Schickert, G., and Winkler, H. (1977). “Results of test concerning strength and strain of concrete subjected to multiaxial compressive stresses.”Deutsher Ausschuss Fur Stahlbeton, Berlin, Germany.
30.
Smith, S. S., Willam, K. J., Gerstle, K. H., and Sture, S.(1989). “Concrete over the top, or: is there life after peak?”Am. Concrete Inst., 86(5), 491–497.
31.
Spooner, D. C., and Dougill, J. W.(1975). “A quantitative assessment of damage sustained in concrete during compressive loading.”Mag. of Concrete Res., 27(92), 155–160.
32.
van Mier, J. G. M.(1985). “Influence of damage orientation distribution on the multiaxial stress strain behaviour of concrete.”Cement and Concrete Res., 15(5), 849–862.
33.
van Mier, J. G. M.(1986). “Multiaxial strain-softening of concrete. Part I: Fracture.”Mat. and Struct., 19(111), 179–190.
34.
Willam, K. J., and Warnke, E. P. (1975). “Constitutive model for triaxial behavior of concrete.”Proc., IABSE Seminar on Concrete Struct. Subjected to Triaxial Stresses, vol. 19, ISMES, Bergamo, Italy.
35.
Willam, K. J., Hurlbut, B., and Sture, S. (1986). “Experimental and constitutive aspects of concrete failure.”Finite element analysis of reinforced concrete structures, Meyer and Okamura, eds., ASCE, New York, N.Y.
36.
Yankelevsky, D. Z., and Reinhardt, H. W.(1987). “Model for cyclic compressive behavior of concrete.”J. Struct. Engrg., ASCE, 113(2), 228–240.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 123 • Issue 11 • November 1997
Pages: 1111 - 1120
Copyright
Copyright © 1997 American Society of Civil Engineers.
History
Published online: Nov 1, 1997
Published in print: Nov 1997
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