Smooth Limit Surfaces for Metals, Concrete, and Geotechnical Materials
Publication: Journal of Engineering Mechanics
Volume 115, Issue 9
Abstract
A limit surface for engineering materials in terms of three invariants of stress is proposed in which the shape of the surface in the deviatoric plane is described as a function of mean pressure. The shape is triangular for small values of mean pressure and circular for large values. The surface contains no corners, intersects the tensile pressure axis at right angles, and asymptotically approaches a constant value for large values of mean pressure. Since the limit surface is smooth and convex, a scaled version is suitable for the yield surface of an associated plasticity theory with no special algorithm needed for corners. Traditional surfaces are obtained as special cases, and examples of fits to existing experimental data are given.
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References
1.
Bresler, B., and Pister, K. S. (1958). “Strength of concrete under combined stress.” J. Amer. Concrete Inst., 321–345.
2.
Casey, J., and Jahedmotlagh, H. (1984). “The strength‐differential effect in plastieity.” Int. J. Solids and Struct. 20(4), 377–393.
3.
Chen, W. F. (1982). Plasticity in reinforced concrete. McGraw‐Hill Book Co., Inc., New York, N.Y.
4.
de Borst, R. (1986). “Non‐linear analysis of frictional materials,” thesis presented to the Delft University of Technology, Delft, The Netherlands, in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
5.
Drucker, D. C., and Prager, W. (1952). “Soil mechanics and plasticity analysis of limit design.” Quart. Appl. Math. 10, 157–165.
6.
Faruque, M. O., and Chang, C. J. (1986). “New cap model for failure and yielding of pressure‐sensitive materials.” J. Engrg. Mech., ASCE, 112(10), 1041–1053.
7.
Goode, C. D., and Henny, M. A. (1967). “The strength of concrete under combined shear and direct stress.” Mag. Concrete Res., 19(59), 105–112.
8.
Green, S. J., and Swanson, S. R. (1973). “Static constitutive relations for concrete.” AFWL‐TR‐72‐244, Air Force Weapons Lab., Kirtland Air Force Base, N.M.
9.
Hegemier, G. A., Read, H. E., Murakami, H., Hageman, L. J., and Herrmann, R. G. (1983). “Development of advanced constitutive model for reinforced concrete.” SSS‐R‐83‐6112, S‐Cubed, La Jolla, Calif., Apr.
10.
Lade, P. V. (1977). “Elasto‐plastic stress‐strain theory for cohesionless soil with curved yield surfaces.” Int. J. Solids and Struct., 13, 1019–1035.
11.
Lade, P. V. (1982). “Three parameter failure criterion for concrete.” J. Engrg. Mech., ASCE, 108, 850–863.
12.
Lade, P. V., and Duncan, J. M. (1973). “Cubical triaxial tests on cohesionless soil.” J. Soil Mech. Found., ASCE, 99, 793–812.
13.
Lin, F. B., Bažant, Z. P., Chern, J. C., and Marchertas, A. H. (1987). “Concrete model with normality and sequential identification.” J. Comput. and Struct., 26(6), 1011–1025.
14.
Mills, L. L., and Zimmerman, R. M. (1970). “Compressive strength of plain concrete under multiaxial loading conditions.” J. Amer. Concrete Inst., 802–807.
15.
Ottosen, N. S. (1977). “A failure criterion for concrete.” J. Engrg. Mech., ASCE, 103(EM4), 527–535.
16.
Podgorski, J. (1985). “General failure criterion for isotropic media.” J. Engrg. Mech., ASCE, 111(2), 188–201.
17.
Resende, L., and Martin, J. B. (1985). “Formulation of Drucker‐Prager cap model.” J. Engrg. Mech., ASCE, 111(7), 855–881.
18.
Robison, M. J. (1978). “The strength of Indiana Limestone under multiaxial loading conditions,” thesis presented to the University of Colorado, Boulder, Colo., in partial fulfillment of the requirements for the degree of Master of Science.
19.
Schreyer, H. L. (1983). “A third‐invariant plasticity theory for frictional materials.” J. Struct. Mech., ASCE, 11(2), 177–186.
20.
Schreyer, H. L., and Bean, J. E. (1985). “A third‐invariant viscoplasticity theory for rate‐dependent soils.” J. Geotech. Engrg., ASCE, 111(2), 181–192.
21.
Schreyer, H. L., and Babcock, S. M. (1985). “A third‐invariant plasticity theory for low‐strength concrete.” J. Engrg. Mech., ASCE, 111(4), 545–558.
22.
Spitzig, W. A., Sober, R. J., and Richmond, O. (1975). “Pressure dependence of yielding and associated volume expansion in tempered martensite.” Acta Met. 23, 885–893.
23.
Traina, L. A., Babcock, S. M., and Schreyer, H. L. (1983). “Reduced experimental stress‐strain results for a low‐strength concrete under multiaxial states of stress.” AFWL‐TR‐83‐3, Air Force Weapons Lab., Kirtland Air Force Base, N.M.
24.
Vermeer, P. A., and de Borst, R. (1984). “Non‐associated plasticity for soils, concrete and rock.” Heron, 29(3), 1–64.
25.
Willam, K. J., and Warnke, E. P. (1974). “Constitutive model for the triaxial behavior of concrete.” Proc. Int. Assoc. of Bridge and Struct. Engrs. Seminar on Concrete Struct. Subjected to Triaxial Stresses, Paper III‐1, Gergamo, Italy, May 17–19.
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Copyright © 1989 ASCE.
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Published online: Sep 1, 1989
Published in print: Sep 1989
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