Orthotropic Model of Concrete for Triaxial Stresses
Publication: Journal of Structural Engineering
Volume 112, Issue 1
Abstract
An orthotropic model to predict the ascending and descending parts of the stress‐strain curves of concrete subjected to biaxial or triaxial compressive stresses is presented. The stress‐induced orthotropic material properties are expressed in terms of six constants in the compliance matrix. The six material constants are expressed as functions of stress invariants at ultimate strength. The proposed orthotropic constitutive model depends on the knowledge of the three principal stresses at the maximum strength, which are obtained through the use of a strength criterion (which is sensitive to all the three stress invariants). For predicting the ascending and descending parts of the multiaxial stressstrain curves, the six orthotropic material constants in the compliance matrix are continuously changed with the help of a “fracturing index” parameter. The proposed constitutive model compares favorably with the available experimental data under multiaxial stresses.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ahmad, S. H., and Shah, S. P., “Complete Triaxial Stress‐Strain Curves for Concrete,” Journal of the Structural Division, ASCE, Vol. 108, No. ST4, Apr., 1982, pp. 728–742.
2.
Ahmad, S. H., “Properties of Confined Concrete under Static and Dynamic Loads,” thesis presented to the Univ. of Illinois, at Chicago, IL, in 1981, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
3.
Bathe, K. J., and Ramaswamy, S., “On Three‐Dimensional Nonlinear Analysis of Concrete Structures,” Nuclear Engineering and Design, Vol. 52, No. 3, May, 1979, pp. 385–409.
4.
Bažant, Z. P., “Critique of Orthotropic Models and Triaxial Testing of Concrete and Soils,” Structural Engineering Report No. 79‐10/640C, Northwestern Univ., Evanston, IL, Oct., 1979.
5.
Bažant, Z. P., and Bhat, P. D., “Hysteretic Fracturing Endochronic Theory for Concrete,” Journal of the Engineering Mechanics Division, ASCE, Vol. 106, No. EM5, Oct., 1980, pp. 929–950.
6.
“Behavior of Concrete under Multiaxial State of Stress,” Comite Europeen du Beton, Berlin, Germany, 1984.
7.
Bresler, B., and Pister, K. S., “Strength of Concrete under Combined Stresses,” Journal of the American Concrete Institute, Sept., 1958.
8.
Chen, W. F., and Ting, E. C., “Constitutive Model for Concrete Structure,” Journal of the Engineering Mechanics Division, ASCE, Vol. 106, No. EM1, Feb., 1980, pp. 1–19.
9.
Darwin, D., and Pecknold, D. A., “Nonlinear Biaxial Law for Concrete,” Journal of the Engineering Mechanics Division, ASCE, Vol. 103, No. EM2, Proc. Paper 12839, Apr., 1977, pp. 229–241.
10.
Darwin, D., and Pecknold, D. A., “Analysis of Cyclic Loading of Plane R/C Structures,” Computers and Structures, Vol. 7, Pergamon Press, Inc., New York, NY, 1977, pp. 137–147.
11.
Elwi, A. A., and Murray, D. W., “A 3D Hypoelastic Concrete Constitutive Relationship,” Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM4, Aug., 1979, pp. 623–641.
12.
Ferrara, G., et al., “Dispositivi di prova per l' analisis sperimentale del cornportamento di conglomerati cementizi sotoposti a stati triassiali di sollectaxione,” presented at the 4th AIAS Congress, Rome Italy, Oct., 1976.
13.
Geistefeld, H., “Material Law for Concrete under Multiaxial Stress,” Proceedings of the 4th International Conference on Structural Mechanics in Reactor Technology, held at San Francisco, CA, Aug., 1977 (Vol. H, Paper H5/2, T. A. Jaegan and B. A. Boley, Eds.).
14.
Gerstle, K. H., “Simple Formulation of Triaxial Concrete Behavior,” Journal of the American Concrete Institute, Vol. 78, No. 5, Sept.–Oct., 1981, pp. 382–387.
15.
Gopalaratham, V. S., and Shah, S. P., “Softening Response of Concrete in Direct Tension,” Journal of the American Concrete Institute (in press).
16.
Green, S. J., and Swanson, S. R., “Static Constitutive Relation for Concrete,” Technical Report No. AFWL‐TR‐72‐244 (AD‐761820), Air Force Weapons Laboratory, New Mexico, Apr., 1973.
17.
Kotsovos, M. D., and Newman, J. B., “A Mathematical Description of the Deformation Behavior of Concrete under Complex Loading,” Magazine of Concrete Research, Vol. 31, No. 109, June, 1979, pp. 77–90.
18.
Kotsovos, M. D., and Newman, J. B., “Mathematical Description of Deformational Behavior of Concrete under Generalized Stress beyond Ultimate Strength,” Journal of the American Concrete Institute, Vol. 77, No. 5, Sept.–Oct., 1980, pp. 340–346.
19.
Kupfer, H. B., et al., “Behavior of Concrete under Biaxial Stresses,” Journal of the American Concrete Institute, Vol. 66, No. 8, Aug., 1969, pp. 656–666.
20.
Liu, T. C. Y., Nilson, A. H., and Slate, F. O., “Biaxial Stress‐Strain Relations for Concrete,” Journal of the Structural Division, ASCE, Vol. 98, No. ST5, Proc. Paper 8905, May, 1972, pp. 1025–1034.
21.
Maekawa, K., and Okamura, H., “The Deformational Behavior and Constitutive Equation of Concrete Using the Elasto‐Plastic and Fracture Model,” Journal of the Faculty of Engineering, Univ. of Tokyo, Series B, Vol. XXXVII, No. 2, 1983.
22.
Ottosen, N. S., “Constitutive Model for Short‐Time Loading of Concrete,” Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM1, Feb., 1979, pp. 127–141.
23.
Palaniswamy, R., and Shah, S. P., “Fracture and Stress‐Strain Relation for Concrete under Triaxial Compression,” Journal of the Structural Division, ASCE, Vol. 100, No. ST5, Proc. Paper 10547, May, 1974, pp. 901–916.
24.
“A State‐of‐the‐Art Report on Finite Element Analysis of Reinforced Concrete Structures,” by the Task Committee on Finite Element Analysis of Reinforced Concrete Structures, Committee on Concrete and Masonry Structures, ASCE Special Publication, 1982.
25.
Tasuji, M. E., et al., “Stress‐Strain Response and Fracture of Concrete in Biaxial Loading,” Journal of the American Concrete Institute, Vol. 75, No. 7, July, 1978.
26.
Van Greunen, J., “Nonlinear Geometric, Material and Time‐Dependent Analysis of Reinforced and Prestressed Concrete Slabs and Panels,” SESM Report No. 79‐3, Univ. of California, Berkeley, CA, Oct., 1979.
Information & Authors
Information
Published In
Copyright
Copyright © 1986 ASCE.
History
Published online: Jan 1, 1986
Published in print: Jan 1986
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.