Microplane model M4 for concrete. II: Algorithm and calibration

Ferhun C. Caner*, Zdenek P Bazant

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

117 Scopus citations


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 parameterd, 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.

Original languageEnglish (US)
Pages (from-to)954-961
Number of pages8
JournalJournal of Engineering Mechanics
Issue number9
StatePublished - Sep 1 2000

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


Dive into the research topics of 'Microplane model M4 for concrete. II: Algorithm and calibration'. Together they form a unique fingerprint.

Cite this