Continuous relaxation spectrum for concrete creep and its incorporation into microplane model M4

Goangseup Zi*, Zdeněk P. Bažant

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

27 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1331-1336
Number of pages6
JournalJournal of Engineering Mechanics
Issue number12
StatePublished - Dec 2002


  • Concrete
  • Creep
  • Stress relaxation
  • Triaxial stresses

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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