Endochronic model for nonlinear triaxial behavior of concrete

Zdenek P Bazant*, Shieh Ching-Long Shieh

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


A gradual accumulation of inelastic strain can be most conveniently described in terms of the so-called intrinsic time, whose increment depends on the time increment as well as the strain increments, and was originally developed for metals and was extended in a previous paper by Z.P. Bažant to concrete. In that previous paper it had been demonstrated that the proposed model predicts quite closely: (1) Stress-strain diagrams for concretes of different strength; (2) uniaxial, biaxial and triaxial stress-strain diagrams and failure envelopes; (3) failure envelopes for combined torsion and compression: (4) lateral strains and volume expansion in uniaxial and biaxial tests; (5) the behavior of spirally confined concrete; (6) hysteresis loops for repeated high compression: (7) cyclic creep up to 106 cycles; (8) the strain rate effect; (9) the decrease of long time strength: and (10) the increase of short-time strength due to low stress creep. The present paper presents a refinement of the endochronic theory of concrete which consists mainly in taking into account; (a) the inelastic strains due to hydrostatic compression; (b) improved descriptions of strain-softening behavior, (c) cyclic loading in strain-softening range, and (d) volume change in strain-softening range; (e) the differences between proportional and standard triaxial tests; (f) triaxial failure envelopes; and (g) dependence of material parameters on strength. The formulation consists fully of continuous functions, and for numerical analysis it has the advantage that it contains no inequalities. The present expressions are, admittedly, rather complicated and contain many parameters. However, for computer calculations this is not an insurmountable drawback. The agreement with test data is far superior to any other constitutive law found this far - virtually all currently known basic properties are modeled. The value of all material parameters are given, their dependence on concrete strength is identified, and a broad range of normal weight concrete is covered.

Original languageEnglish (US)
Pages (from-to)305-315
Number of pages11
JournalNuclear Engineering and Design
Issue number2
StatePublished - May 2 1978

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Nuclear Energy and Engineering
  • Materials Science(all)
  • Safety, Risk, Reliability and Quality
  • Waste Management and Disposal
  • Mechanical Engineering


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