Continuous Relaxation Spectrum for Concrete Creep and its Incorporation into Microplane Model M4
Publication: Journal of Engineering Mechanics
Volume 128, Issue 12
Abstract
Efficient numerical finite-element analysis of creeping concrete structures requires the use of Kelvin or Maxwell chain models, which are most conveniently identified from a continuous retardation or relaxation spectrum, the spectrum in turn being determined from the given compliance or relaxation function. The method of doing that within the context of solidification theory for creep with aging was previously worked out by Bažant and Xi in 1995 but only for the case of a continuous retardation spectrum based on the Kelvin chain. The present paper is motivated by the need to incorporate concrete creep into the recently published Microplane Model M4 for nonlinear triaxial behavior of concrete, including tensile fracturing and behavior under compression. In that context, the Maxwell chain is more effective than the Kelvin chain, because of the kinematic constraint of the microplanes used in M4. The paper shows how to determine the continuous relaxation spectrum for the Maxwell chain, based on the solidification theory for aging creep of concrete. An extension to the more recent microprestress-solidification theory is also outlined and numerical examples are presented.
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References
Bažant, Z. P. (1971). “Numerically stable algorithm with increasing time steps for integral type aging creep.” Proc., 1st International Conf. on Structural Mechanics in Reactor Technology, BAM, 4, H2/3.
Bažant, Z. P. (1975). “Theory of creep and shrinkage in concrete structures: A precis of recent developments.” Mechanics today, S. Nemat-Nasser, ed., American Academy of Mechanics, Vol. 2, New York, Pergamon, 1–93.
Bažant, Z. P. (1982). “Mathematical models for creep and shrinkage of concrete.” Creep and shrinkage in concrete structures, Z. P. Bažant and F. H. Wittmann, eds., Chap. 7, Wiley, London, 163–256.
Bažant, Z. P. (1984). “Microplane model for strain controlled inelastic behavior.” Mechanics of engineering materials, C. S. Desai and R. H. Gallagher, eds, Chap. 3, J. Wiley, London, 45–59.
Bažant, Z. P. (2001). “Creep of Concrete.” Encyclopedia of materials: Science and technology, Vol. 2C, Elsevier, Amsterdam, 1797–1800.
Bažant, Z. P., and Baweja, S.(1995), in collaboration with RILEM Committee TC 107-GCS, “Creep and shrinkage prediction model for analysis and design of concrete structures—model B3” (RILEM Recommendation) Mater. Struct., 28, 357–365; with Errata, Vol. 29 (March 1996), p. 126.
Bažant, Z. P., and Baweja, S. (2000). “Creep and shrinkage prediction model for analysis and design of concrete structures: Model B3—short form.” Adam Neville Symposium: Creep and Shrinkage-Structural Design Effects, ACI SP-194, A. Al-Manaseer, ed., American Concrete Institute, Farmington Hills, Mich., 85–100.
Bažant, Z. P., Caner, F. C., Carol, I., Adley, M. D., and Akers, S. A.(2000a). “Microplane model M4 for concrete. I: Formulation with work-conjugate deviatoric stress.” J. Eng. Mech., 126(9), 944–953.
Bažant, Z. P., Caner, F. C., Adley, M. D., and Akers, S. A.(2000b). “Fracture rate effect and creep in microplane model for dynamics.” J. Eng. Mech., 126(9), 962–970.
Bažant, Z. P., Hauggaard, A. B., and Baweja, S.(1997). “Microprestress-solidification theory for concrete creep. II: Algorithm and verification.” J. Eng. Mech., 123(11), 1195–1201.
Bažant, Z. P., and Kim, S. S.(1979). “Approximate relaxation function for concrete.” J. Struct. Div. ASCE, 105(12), 2695–2705.
Bažant, Z. P., and Prasannan, S.(1989). “Solidification theory for concrete creep. II: Verification and application.” J. Eng. Mech., 115(8), 1704–1725.
Bažant, Z. P., and Prat, P. C.(1988). “Microplane model for brittle-plastic material. I: Theory.” J. Eng. Mech., 114(10), 1672–1688.
Bažant, Z. P., and Xi, Y.(1995). “Continuous retardation spectrum for solidification theory of concrete creep.” J. Eng. Mech., 121(2), 281–288.
Bažant, Z. P., Xiang, Y., and Prat, P. C.(1996). “Microplane model for concrete. I: Stress-strain boundaries and finite strain.” J. Eng. Mech., 122(3), 245–254 (with Errata, Vol. 123(3), p. 411).
Caner, F. C., and Bažant, Z. P.(2000). “Microplane model M4 for concrete. II: Algorithm and calibration.” J. Eng. Mech., 126(9), 954–961.
Carol, I., and Bažant, Z. P.(1993). “Viscoelasticity with aging caused by solidificaton of nonaging constituent.” J. Eng. Mech., 119(11), 2252–2269.
Carol, I., and Bažant, Z. P.(1997). “Damage and plasticity in microplane theory.” Int. J. Solids Struct., 34(29), 3807–3835.
Carol, I., Bažant, Z. P., and Prat, P. C.(1991). “Geometric damage tensor based on microplane model.” J. Eng. Mech., 117(10), 2429–2448.
Jirásek, M. (2000). “Nonlinear time-dependent material model for concrete.” LSC Internal Rep. No. 00/01, Swiss Federal Institute of Technology (EPFL).
RILEM Committee TC 69. (1988). (Z. P. Bažant, Chairman and principal author), “State of the art in mathematical modeling of creep and shrinkage of concrete.” Mathematical Modeling of Creep and Shrinkage of Concrete, Z. P. Bažant, ed., Wiley, Chichester, 1988, 57–215; and in preliminany form: “State-of-art report on creep and shrinkage of concrete: Mathematical modeling.” Preprints, 4th RILEM Int. Conf. on Creep and Shrinkage of Concrete, 1986, Z. P. Bažant, ed. 41–80.
Trost, H.(1967). “Auswirkungen des superpositionsprinzips auf kriech-und relaxations-probleme bei beton spannbeton.” Beton Stahlbetonbau, 62, 230–238.
Tschoegl, N. W. (1989). The phenomenological theory of linear viscoelastic behavior, Springer, Berlin.
Widder, D. V. (1971). An introduction to transformation theory, Academic, New York.
Zi, G., and Bažant, Z. P. (2001). “Continuous relaxation spectrum of concrete creep and its incorporation into microplane model M4.” Creep, Shrinkage and Durability Mechanics of Concrete and Other Quasi-Brittle Materials, Proc., 6th Int. Conf., CONCREEP-6, held at MIT, Cambridge), F.-J. Ulm, Z. P. Bažant and F. H. Wittmann, eds., Elsevier, Amsterdam 2001, 239–243.
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Published In
Journal of Engineering Mechanics
Volume 128 • Issue 12 • December 2002
Pages: 1331 - 1336
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Oct 29, 2001
Accepted: Mar 21, 2002
Published online: Nov 15, 2002
Published in print: Dec 2002
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