Mathematical Modeling of Creep and Shrinkage of Concrete Edited by Zdenek P. Bazant Professor of Civil Engineering Northwestern University. Evanston. Illinois. USA In collaboration with International Union of Research and T.esting Laboratories for Materials and Structures (RILEM) and U.S. National Science Foundation A Wiley-Interscience Publication JOHN WILEY AND SONS Chichester . New York . Brisbane . Toronto . Singapore Mathematical Modeling of Creep and Shrinkage of Concrete Edited by Z. Bazant .£) 1988 John Wiley & Sons Ltd Chapter 2 Material Models for Structural Creep Analysis t 2.1 INTRODUCTION Creep and shrinkage of concrete is an intricate phenomenon, and a constitutive equation which is both generally applicable and realistic is difficult to formulate. Before the computer era, this task was not really an issue because no structural analysis problems could be solved with a sophisticated constitutive model. After 1970, however, large computer codes that could accept a complicated constitu- tive model became available. Yet nothing useful could be done with these large codes if a good constitutive model was unavailable. Thus, computers have been providing an impetus for development of realistic constitutive relations for concrete creep and shrinkage, and tremendous progress has taken place during the last fifteen years. . The purpose of this chapter is to review the progress, spell out the fundamental concepts, and emphasize some recent developments that are just becoming ready for computational applications. Since two comprehensive reviews of a similar nature appeared several years ago (ASCE, 1982; Bazant, 1982b), the subjects discussed in depth in these reviews will be covered concisely, while the most recent developments, such as the modeling of creep at variable humidity, will be covered in more detail. 2.2 CONCRETE AS AGING VISCOELASTIC MATERIAL 2.2.1 Compliance function The total strain of a uniaxially loaded concrete specimen at age t may be subdivided as e(t) = cElt) + Edt) + Es(t) + ET(t) = edt) + e"(t) = EE(t) + edt) + EO(t) = eu(t) + eO(t) (2.1) in which edt) is the instantaneous strain, which is elastic (reversible) if the stress is t Principal author: Z. P. BaZant. Prepared by RILEM TC69 Subcommittee 2, the members of which were Z. P. Bazant (Chairman), J. Dougill, C. Huet, T. Tsubaki. and F. Wittmann. 99
Mathematical Modeling of Creep and Shrinkage of Concrete
May 22, 2023
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