Microplane model M5f for multiaxial behavior and fracture of fiber-reinforced concrete

Alessandro Beghini, Zdeněk P. Bažant*, Yong Zhou, Olivier Gouirand, Ferhun C. Caner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

40 Scopus citations


Despite impressive advances, the existing constitutive and fracture models for fiber-reinforced concrete (FRC) are essentially limited to uniaxial loading. The microplane modeling approach, which has already been successful for concrete, rock, clay, sand, and foam, is shown capable of describing the nonlinear hardening-softening behavior and fracturing of FRC under not only uniaxial but also general multiaxial loading. The present work generalizes model M5 for concrete without fibers, the distinguishing feature of which is a series coupling of kinematically and statically constrained microplane systems. This feature allows simulating the evolution of dense narrow cracks of many orientations into wide cracks of one distinct orientation. The crack opening on a statically constrained microplane is used to determine the resistance of fibers normal to the microplane. An effective iterative algorithm suitable for each loading step of finite element analysis is developed, and a simple sequential procedure for identifying the model parameters from test data is formulated. The model allows a close match of published test data on uniaxial and multiaxial stress-strain curves, and on multiaxial failure envelopes.

Original languageEnglish (US)
Pages (from-to)66-75
Number of pages10
JournalJournal of Engineering Mechanics
Issue number1
StatePublished - Jan 2007


  • Concrete, reinforced
  • Fracture
  • Numerical models
  • Stress strain relations

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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