Constitutive Equations for Concrete in Failure State
Publication: Journal of Engineering Mechanics
Volume 115, Issue 8
Abstract
For concrete, two simple three‐dimensional failure conditions depending on the first invariant of the stress tensor as well as on the second and third invariant of the stress deviator tensor with two and four material parameters and a nonassociated flow rule are proposed in this paper. First, the basic equations like stress deviator tensor and invariants of the stress tensor and a stress deviator tensor are introduced. Then the proposed failure conditions are presented in a geometrically interpretable form. In the next step, the material parameters are determined by fitting the failure conditions to several test results. Finally, a nonassociated flow rule is introduced. An example illustrates the usefulness of the proposed constitutive equations in the failure state.
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References
1.
Boswell, L. F., and Chen, Z. (1987). “A general failure criterion for plain concrete.” Int. J. Solid Structs., 23(5), 621–630.
2.
Balmer, G. G. (1949). “Shearing strength of concrete under high triaxial stress‐computation of Mohrs envelope as a curve.” Struct. Res. Lab. Rept. No. SP‐23, Dept. of the Interior, Bureau of Reclamation, Washington, D.C.
3.
Chen, W. F. (1982). Plasticity of reinforced concrete. McGraw‐Hill Book Co., New York, N.Y.
4.
Chen, W. F., and Drucker, D. C. (1969). “Bearing capacity of concrete blocks or rock.” J. Engrg. Mech., ASCE, 95(4), 955–978.
5.
Dais, J. L. (1970). “An isotropic frictional theory for a granular medium with and without cohesion.” Int. J. Solids Structs., 6, 1185–1191.
6.
de Boer, R. (1982). Vektor‐ und tensorrechnung für ingenieure. Springer‐Verlag, Berlin, West Germany (in German).
7.
de Boer, R. (1988). “On plastic deformation of soils.” Int. J. Plasticity, 4.
8.
Dresenkamp, H.‐T. (1987). “Stoffgleichungen für spröde und granulare Stoffe im Bruchzustand.” Thesis presented to the Universität Essen, at Essen, West Germany, in partial fulfillment of the requirements for the degree of Doctor of Philosophy (in German).
9.
Drucker, D. C., and Prager, W. (1952). “Soil mechanics and plasticity analysis of limit design.” Quart. Appl. Math., 10, 157–165.
10.
Gollub, W. (1988). “Grenzen und möglichkeiten der mohr‐coulombschen bruchbedingung.” Thesis presented to the Universität Essen, at Essen, West Germany, in partial fulfillment of the requirements for the degree of Doctor of Philosophy (in German).
11.
Green, A. E., and Naghdi, P. M. (1965). “A general theory of an elastic‐plastic continuum.” Arch. Rational Mech. Anal., 18, 251–281.
12.
Gudehus, G. (1973). “Elastoplastische stoffgleichungen für trockenen sand.” Ingenieur Archiv, 42, 151–169 (in German).
13.
Lade, P. V., and Duncan, J. M. (1975). “Elastoplastic stress‐strain theory for cohesionless soil.” J. Geotech. Engrg., ASCE, 101, 1037–1053.
14.
Lade, P. V. (1982). “Three parameter failure criterion for concrete.” J. Engrg. Mech., ASCE, 108, 850–863.
15.
Launay, P., and Gachon, H. (1972). “Strain and ultimate strength of concrete under triaxial stress.” Amer. Concr. Inst. Spec. Publ. 34, paper 13.
16.
Mills, L. L., and Zimmerman, R. M. (1970). “Compressive strength of plain concrete under multiaxial loading conditions.” J. Amer. Concr. Inst., 67(10), 802–807.
17.
Ottosen, N. S. (1977). “A failure criterion for concrete.” J. Engrg. Mech., ASCE, 103(4), 527–535.
18.
Richardt, F. E., Brandzaeg, A., and Brown, R. L. (1928). “A study of the failure of concrete under combined compressive stresses.” Bulletin No 185, Univ. of Illinois Engrg. Exp. Sta.
19.
Schickert, G., and Winkler, H. (1977). “Versuchsergebnisse zur festigkeit und verformung von beton bei mehraxialer druckbeanspruchung.” Bundesanstalt für Materialprüfung, Deutscher Ausschuβ für Stahlbeton, paper 277, Berlin, West Germany (in German).
20.
Traesdell, C., and Toupin, R. (1960). “The classical field theories.” Handbuch der Physik 3, Springer‐Verlag, Berlin, West Germany.
21.
Vardoulakis, I., Goldscheider, M., and Gudehus, G. (1978). “Formation of shear bands in sand bodies as a bifurcation problem.” Int. J. for Numerical and Analyt. Meth. in Geomech., 2, 99–128.
22.
Willam, K. J., and Warnke, E. P. (1975). “Constitutive models for the triaxial behaviour of concrete.” Int. Assoc. Bridge Struct. Engrg. Proc., 19, 1–30.
23.
Winselmann, D. (1984). “Stoffgesetze mit isotropischer und kinematischer verfestigung sowie deren anwendung auf sand.” Bericht Nr. 84‐44, Institut für Statik der Technischen Universität Braunschweig, West Germany.
Information & Authors
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Published In
Journal of Engineering Mechanics
Volume 115 • Issue 8 • August 1989
Pages: 1591 - 1608
Copyright
Copyright © 1989 ASCE.
History
Published online: Aug 1, 1989
Published in print: Aug 1989
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