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A concrete plasticity model with elliptic failure surface and independent hardening/softening

  • Al-Ghamedy, Hamdan N. (Dep. of Civil Engineering, King Fahd University of Petroleum & Minerals)
  • Published : 1994.03.25

Abstract

A plasticity-based concrete model is proposed. The failure surface is elliptic in the ${\sigma}-{\tau}$ stress space. Independent hardening as well as softening is assumed in tension, compression, and shear. The nonlinear inelastic action initiates from the origin in the ${\sigma}-{\varepsilon}$(${\tau}-{\gamma}$) diagram. Several parameters are incorporated to control hardening/softening regions. The model is incorporated into a nonlinear finite element program along with other classical models. Several examples are solved and the results are compared with experimental data and other failure criteria. "Reasonable results" and stable solutions are obtained for different types of reinforced concrete oriented structures.

Keywords

References

  1. Bazant, Z.P. and Shieh, C.L. (1978), "Endochronic models for nonlinear triaxial behavior of concrete", Nuclear Engineering and Design, 47, 305-315. https://doi.org/10.1016/0029-5493(78)90074-2
  2. Blaauwendraad, J., Berg, F.J. and Merks, P.J. (1983), "Bench mark problems", Rijkwaterstaat Structural Research, Delft University.
  3. Bresler, B. and Pister, K.S. (1958), "Strength of concrete under combined stresses", J. ACI, 55, 321-345.
  4. Chen, W.F. and Saleeb, A.F. (1982), "Constitutive equations for engineering materials", 1, Elasticity and Modeling, John Wiley and Sons, New York.
  5. Chen, A.C.T. and Chen, W.F. (1975), "Constitutive relations for concrete", J. Eng. Mech. Div., ASCE, 101(EM4), 465-481.
  6. Chen, W.F. (1982), Plasticity in Reinforced Concrete, McGraw-Hill, New York.
  7. Chiarito, V.P. and Wright, R.S. (1984), Ultimate Behavior of Reinforced Concrete Circular Conduits, Struct. Mech. Div., Structures Laboratory, USAE Waterways Experiment Station, Vicksburg, Mississippi.
  8. Committee on Concrete and Masonry Structures, State of the Art Report on Finite Element Analysis of Reinforced Concrete, Chapter 2-Constitutive Relations and Failure Theories, Task Committee on Finite Element Analysis of Reinforced Concrete Structures(Arthur H. Nilson, Chairman), ASCE 1982.
  9. Day, S.E. (1985), "A softening plasticity model for concrete", M.S. Thesis, CEAE Department, University of Colorado, Boulder.
  10. Desai, C.S. and Siriwardane, H.J. (1984), Constitutive Laws for Engineering Materials with Emphasis on Geologic Materials, Prentice-Hall Inc., Englewood Cliffs, NJ.
  11. Elwi, A.A. and Murray, D.W. (1979), "A 3D hypoelastic concrete constitutive relationship", J. Eng. Mech. Div., ASCE, 105(EM4), 623-641.
  12. Epstein, M. and Murray, D.W. (1978), "A biaxial law for concrete incorporated in BOSORS Code", Computers & Structures, 9(1), 57-63. https://doi.org/10.1016/0045-7949(78)90058-5
  13. Fanella, D.A. (1990), "Fracture and failure of concrete in uniaxial and biaxial loading", J. Eng. Mech., ASCE, 116(11), 2341-2362. https://doi.org/10.1061/(ASCE)0733-9399(1990)116:11(2341)
  14. Franz, G. and Brenker, H. (1967), "Verformungsuersche an stahlbetonbalken mit hochfestem bewehrungsstahl", Heft, 188, Von Wilhelm Ernst & Sohn, Deutscher Ausschuss fur Stahlbeton, Berlin.
  15. Gerstle, K.H., Aschi, H., Bellotti, R., Bertacchi, P., Kotsovos, M.D., Ko, H.Y., Linse, D., Newman, J.B., Russi, P., Schickert, G., Taylor, M.A., Traina, L.A., Winkler, H. and Zimmerman, R.M. (1980), "Behavior of concrete under multiaxial stress states", J. Eng. Mech. Div., ASCE, 106, 1383-1403.
  16. Gerstle, K.H. (1985), "Analytical study of WES ring tests", Structural Research Series 8504, CEAE Department, University Colorado, Boulder.
  17. Ghamedy, H.N. (1986), "Nonlinear finite element analysis of inelastic structures with applications to reinforced concrete", Ph.D Dissertation CEAE Department, University of Colorado, Boulder.
  18. Al-Ghamedy, H.N. and Willam, K.J. (1990), "Layered nonhomogeneous curved beam elements for inelastic analysis", Computers & Structures, 37(4), 521-534. https://doi.org/10.1016/0045-7949(90)90041-Y
  19. Hurlbut, B.S. (1985), "Experimental and computational investigation of strain softening in concrete", M.S. Thesis, CEAE Department, University of Colorado.
  20. 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", J. ACI, 60(2), 209-224.
  21. Kotsovos, M.D. and Newman, J.B., (1977), "Behavior of concrete under multiaxial stress", J. ACI, 74(9), 443-446
  22. Kotsovos, M.D. and Newman, J.B. (1978), "Generalized stress-strain relations for concrete", J. Eng. Mech. Div., ASCE, 104 (EM4), 843-856.
  23. Krajcinovic, D. and Fonseka, G.V. (1981), "The continuous damage theory of brittle materials, Part 1: General theory", ASME Trans., Journal of Applied Mechanics, 4(4), 809-815.
  24. Lade, P.V. and Nelson, R.B. Desai, (1981), "Incrementalization procedure for elasto-plastic constitutive model with mutiple, simultaneous yield surfaces", In: Implementation of Computer Procedures and Stress-Strain Laws in Geotechnical Engineering, II,(Desai, C.S., Saxena, S.K., eds.), Acorn Press.
  25. Levine, H.S. (1982), "A two-surface plastic and microcracking model for plain concrete", Nonlinear Numerical Analysis of Reinforced Concrete, Winter Annual Meeting, ASME, Phoenix, Az, Nov. 14-19, 1982, 27-47.
  26. Murray, D.W., Chituyanondh, L.;Rijub-Agha, K.Y. and Wong, C. (1979), "A concrete plasticity theory for biaxial stress analysis", J. Eng. Mech. Div., ASCE, 105(GM6), 989-1106.
  27. Ottosen, N.S. (1977), "A failure criterion for concrete", J. Eng. Mech. Div., ASCE, 103(EM4), 527-535.
  28. Nayak, G.C. and Zienkiewicz, O.C. (1972), "Elasto-plastic stress analysis generalization of various constitutive relations including strain softening", Int. Journal for Numerical Methods in Engineering, 5, 113-135. https://doi.org/10.1002/nme.1620050111
  29. Sargin, M. (1971), Stress-strain relationships for concrete and the analysis of structural concrete sections, Study No.4, Solid Mech. Div., University of Waterloo, Canada.
  30. Scavuzzo, R., Stankowski, T., Gerstle, K.H. and Ko, H.Y. (1983), "Stress-strain curves for concrete under multiaxial load histories", Report, University of Colorado, Boulder.
  31. Stankowski, T. and Gerstle, K.H. (1985), "Simple formulation of concrete behavior under multiaxial load histories", J. ACI, 82(2), 213-221.
  32. Stankowski, T. (1980), Grenzlastanalyse eines stahlbetonbalkens mit der F.E. methode, Duplom-Arbeit, Inst. Fuer Massivbau, University Stuttgart, Germany.
  33. Stevens, N.J. Uzumeri, S.M., Collins, M.P. and Will, G.T. (1991), "Constitutive model for reinforced concrete finite element analysis", ACI Structural Journal, 88 (1), 49-59.
  34. Tasuji, M.E., Slate, F.O. and Nilson, A.H. (1978), "Stress-strain response and fracture of concrete in biaxial loading", J. ACI, 75 (7), 306-312.
  35. van Mier, J.G.M. (1984), "Strain-softening of concrete under multiaxial loading conditions", Ph.D. Dissertation, University of Technology, Eindhoven.
  36. Walraven, J.C. (1982), "The influence of depth on the shear strength of lightweight concrete beams without shear reinforcement", Stevin Laboratory, Report No. 5-78-4, Delft University of Technology, Delft, The Netherlands.
  37. Willam, K.J. and Sture, S. (1986), "Finite elements and localized failure: Final technical report", Structural Research Series 8601, CEAE Department, University of Colorado, Boulder.
  38. Willam, K.J., Bicanic, N. and Sture, S. (1984), "Constitutive and computational aspects of strain-softening and localization in solids", Symp. on Constitutive Equations, Macro and Computational Aspects, ASME/WAM 84 Meeting, New Orleans, ASME (Willam, K., ed.), G00274, New York, 233-252.
  39. Willam, K.J., Hurlbut, B. and Sture, S. (1985), "Experimental, constitutive and computational aspects of concrete failure", Proc. U.S.-Japan Joint Seminar on Finite Element analysis of Reinforced Concrete Structures, 1, University of Tokyo, May 21-24, 1985, 149-171.
  40. Willam, K.J. (1984), "Experimental and computational aspect of concrete fracture", Int. Conf. Computer-Aided Analysis and Design of Concrete Structures, Split, Yugoslavia, September 17-21, 1984, 33-69.
  41. Willam, K., Bicanic, N., Pramono, E. and Sture, S. (1986), "Composite fracture model for strain-softening computation of concrete failure", Proc. Int. Conf. Fracture Mechanics of Concrete-Fundamentals and Applications, EPF Lausanne, Switzerland, October 1-3, 1985, Elsevier Publ., Amsterdam.
  42. Willam, K.J. and Warnke, E.P. (1975), "Constitutive models for the triaxial behavior of concrete", Int. Assoc. Bridge Struct. Eng. Sem. Concr. Struc. Subjected Triaxial Stresses, Bergamo, Italy, 1974, Int. Assoc. Bridge Struct. Eng. Proc., 19, 1-30.
  43. Willam, K.J., Pramono, E. and Sture, S. (1985), "Stability and uniqueness of strain-softening computations", Europe-US Symposium on Finite Element Methods for Nonlinear Problems, NIT Trondheim, August 12-16, 1985, Structural Research Series 8503, University of Colorado, Boulder. 1-24.
  44. Wright, R.S. and Chiarito, V.P. (1984), The Effect of Confining Pressures on the Behavior of Reinforced Concrete Circular Conduits, Struct. Mech. Div., Structures Laboratory, USAE Waterways Experiment Station, Vicksburg, Mississippi.
  45. Yoder, P.J. and Iwan, W.D. (1981), "On the formulation of strain-space plasticity with multiple loading surfaces", ASME Trans., Journal of Applied Mechanics, 48 (4), 773-778. https://doi.org/10.1115/1.3157732