Microplane model for progressive fracture of concrete and rock

Zdeněk P. Bažant, Byung H. Oh

Research output: Contribution to journalArticlepeer-review

317 Scopus citations


A constitutive model for a brittle aggregate material that undergoes progressive tensile fracturing or damage is presented. It is assumed that the normal stress on a plane of any orientation within the material, called the microplane, is a function of only the normal strain on the same microplane. This strain is further assumed to be equal to the resolved component of the macroscopic strain tensor, while the stress on the microplane is not equal to the resolved component of the macroscopic stress tensor. The normal strain on a microplane may be interpreted as the sum of the elastic strain and of the opening widths (per unit length) of all microcracks of the same orientation as the microplane. An additional volumetric elastic strain is introduced to adjust the elastic Poisson ratio to a desired value. An explicit formula which expresses the tangent stiffness of the material as an integral over the surface of a unit hemisphere is derived from the principle of virtual work. The model can represent experimentally observed uniaxial tensile strain-softening behavior, and the stress reduces to zero as the strain becomes sufficiently large. Due to various combinations of loading and unloading on individual microplanes, the response of the model is path-dependent. Since the tensorial invariance restrictions are always satisfied by the microplane system, the model can be applied to progressive fracturing under rotating principal stress directions. This type of application is the main purpose of the model.

Original languageEnglish (US)
Pages (from-to)559-582
Number of pages24
JournalJournal of Engineering Mechanics
Issue number4
StatePublished - Apr 1985

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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