Numerical smeared fracture analysis: Nonlocal microcrack interaction approach

Joško Ožbolt*, Zdenek P Bazant

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

71 Scopus citations


A recently proposed new nonlocal concept based on microcrack interactions is discussed, its implementation in a smeared cracking finite element code for concrete is presented, numerical studies are reported, and comparisons with experimental results are made. He nonlocality is not merely a mathematical device to prevent excessive spurious localization into a zone of zero volume but is a necessary physical consequence of microcrack interactions. Since the constitutive law itself is strictly local, the new nonlocal concept can be combined with any type of constitutive law for strain-softening nonlocal damage, which is here chosen to be the microplane model. A simple method is formulated to approximately identify the material parameters in the model from the basic characteristics of concrete such as the tensile strength, fracture energy and maximum um aggregate size. The results of finite element analysis are shown to be mesh insensitive, and good convergence is obtained. Cracking damage is found to localize into a volume whose size and shape depend on the macroscopic concrete properties as well as the current stress-strain state. Although the damage is considered to be tensile on the microlevel, due solely to mode I microcracks, the new nonlocal model can describe well not only mode I fracture tests but also complex shear-dominated and mixed-mode types of failure such a diagonal shear, and can do so for the same values of material parameters (which was not the case for previous nonlocal models). Most importantly, the new nonlocal model can correctly capture the size effect of quasibrittle fracture, in approximate agreement with Bažant's size effect law.

Original languageEnglish (US)
Pages (from-to)635-661
Number of pages27
JournalInternational Journal for Numerical Methods in Engineering
Issue number4
StatePublished - Jan 1 1996


  • Concrete structures
  • Damage
  • Finite element analysis
  • Fracture
  • Microcracking
  • Nonlocal models

ASJC Scopus subject areas

  • Numerical Analysis
  • Engineering(all)
  • Applied Mathematics


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