Microplane Model M4 for Concrete. II: Algorithm and Calibration
Publication: Journal of Engineering Mechanics
Volume 126, Issue 9
Abstract
This paper represents Part II of a two-part study in which a new improved version of the microplane constitutive model for damage-plastic behavior of concrete in 3D is developed. In Part II, an explicit numerical algorithm for model M4 is formulated, the material parameters of model M4 are calibrated by optimum fitting of the basic test data available in the literature, and the model is verified by comparisons with these data. The data in which strain localization must have occurred are delocalized, and the size effect is filtered out from the data where necessary. Although model M4 contains many material parameters, all but four have fixed values for all types of concretes. Thus the user needs to adjust only four free material parameters to the data for a given concrete, for which a simple sequential identification procedure is developed. If the user's data consist only of the standard compression strength and the strain at uniaxial stress peak, the adjustment is explicit and immediate. Good agreement with an unusually broad range of material test data is achieved.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Aschl, H., Linse, D., and Stöckl, S. (1976). “Strength and stress-strain behavior of concrete under multiaxial compression and tension loading.” Tech. Rep., Technische Universität München, Germany.
2.
Balmer, G. G. (1949). “Shearing strength of concrete under high triaxial stress—Computation of Mohr's envelope as a curve.” Struct. Res. Lab. Rep. No. SP-23, U.S. Department of the Interior and Bureau of Reclamation, Denver.
3.
Bažant, Z. P., et al. (2000a). “Large-strain generalization of microplane model for concrete and application.”J. Engrg. Mech., ASCE, 126(9), 971–980.
4.
Bažant, Z. P., Bishop, F. C., and Chang, T.-P. (1986). “Confined compression tests of cement paste and concrete up to 300 ksi.” J. Am. Concrete Inst., 33(4), 553–560.
5.
Bažant, Z. P., Caner, F. C., Carol, I., Adley, M. D., and Akers, S. A. (2000c). “Microplane model M4 for concrete: I: Formulation with work-conjugate deviatoric stress.”J. Engrg. Mech., ASCE, 126(9), 944–953.
6.
Bažant, Z. P., Caner, F. C., Adley, M. A., and Akers, S. A. (2000b). “Fracturing rate effect and creep in microplane model for dynamics.”J. Engrg. Mech., ASCE, 126(9), 962–970.
7.
Bažant, Z. P., and Cedolin, L. (1991). Stability of structures: Elastic, inelastic, fracture and damage theories, Oxford University Press, New York.
8.
Bažant, Z. P., and Ožbolt, J. (1990). “Nonlocal microplane model for fracture, damage, and size effect in structures.”J. Engrg. Mech., ASCE, 116(11), 2485–2505.
9.
Bažant, Z. P., and Prat, P. C. (1988a). “Microplane model for brittle plastic material. I: Theory.”J. Engrg. Mech., ASCE, 114(10), 1672–1688.
10.
Bažant, Z. P., and Prat, P. C. (1988b). “Microplane model for brittle plastic material. II: Verification.”J. Engrg. Mech., ASCE, 114(10), 1689–1699.
11.
Bažant, Z. P., Xiang, Y., Adley, M. D., Prat, P. C., and Akers, S. A. (1996a). “Microplane model for concrete. II: Data delocalization and verification.”J. Engrg. Mech., ASCE, 122(3), 255–262.
12.
Bažant, Z. P., Xiang, Y., and Prat, P. C. (1996b). “Microplane model for concrete. I: Stress-strain boundaries and finite strain.”J. Engrg. Mech., ASCE, 122(3), 245–254.
13.
Bresler, B., and Pister, K. S. (1958). “Strength of concrete under combined stresses.” J. Am. Concrete Inst., 551(9), 321–345.
14.
Cofer, W. F., and Kohut, S. W. (1994). “A general nonlocal microplane concrete material model for dynamic finite element analysis.” Comp. and Struct., 53(1), 189–199.
15.
Goode, C. D., and Helmy, M. A. (1967). “The strength of concrete under combined shear and direct stress.” Mag. of Concrete Res., 1959, 105–112.
16.
Green, S. J., and Swanson, S. R. (1973). “Static constitutive relations for concrete.” Rep. No. AFWL-TR-72-2, Air Force Weapons Lab., Kirtland Air Force Base, Albuquerque, N.M.
17.
Kupfer, H., Hilsdorf, H. K., and Rüsch, H. (1969). “Behavior of concrete under biaxial stresses.” J. Am. Concrete Inst., 66, 656–666.
18.
Launay, P., and Gachon, H. (1971). “Strain and ultimate strength of concrete under triaxial stress.” Proc., 1st Int. Conf. on Struct. Mech. in Reactor Technol. (SMiRT1), T. Jaeger, ed., Commission of European Communities, Brussels.
19.
Ožbolt, J., and Bažant, Z. P. (1996). “Numerical smeared fracture analysis: Nonlocal microcrack interaction approach.” Int. J. Numer. Methods in Engrg., Chichester, U.K., 39, 635–661.
20.
Petersson, P. E. (1981). “Crack growth and development of fracture zones in plain concrete and similar materials.” Rep. No. TVBM 1006, Lund Institute of Technology, Lund, Sweden.
21.
Reinhardt, H. W., and Cornelissen, H. A. W. (1984). “Post-peak cyclic behavior of concrete in uniaxial tensile and alternating tensile and compressive loading.” Cement and Concrete Res., 14(2), 263–270.
22.
Sinha, B. P., Gerstle, K. H., and Tulin, L. G. (1964). “Stress-strain relations for concrete under cyclic loading.” J. Am. Concrete Inst., 62(2), 195–210.
23.
van Mier, J. G. M. ( 1984). “Strain-softening of concrete under multiaxial loading conditions.” PhD dissertation, De Technische Hogeschool Eindhoven, The Netherlands.
24.
van Mier, J. G. M. (1986). “Multiaxial strain-softening of concrete. I: Fracture; II: Load histories.” Mat. and Struct., 111(19), 179–200.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 126 • Issue 9 • September 2000
Pages: 954 - 961
History
Received: Mar 2, 1999
Published online: Sep 1, 2000
Published in print: Sep 2000
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.