Equivalent localization element for crack band approach to mesh-sensitivity in microplane model

Jan Červenka, Zdeněk P. Bažant*, Martin Wierer

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

62 Scopus citations


The paper presents in detail a novel method for finite element analysis of materials undergoing strain-softening damage based on the crack band concept. The method allows applying complex material models, such as the microplane model for concrete or rock, in finite element calculations with variable finite element sizes not smaller than the localized crack band width (corresponding to the material characteristic length). The method uses special localization elements in which a zone of characteristic size, undergoing strain softening, is coupled with layers (called 'springs') which undergo elastic unloading and are normal to the principal stress directions. Because of the coupling of strain-softening zone with elastic layers, the computations of the microplane model need to be iterated in each finite element in each load step, which increases the computer time. Insensitivity of the proposed method to mesh size is demonstrated by numerical examples. Simulation of various experimental results is shown to give good agreement.

Original languageEnglish (US)
Pages (from-to)700-726
Number of pages27
JournalInternational Journal for Numerical Methods in Engineering
Issue number5
StatePublished - Feb 7 2005


  • Concrete
  • Damage
  • Finite elements
  • Fracture
  • Localization
  • Microplane model

ASJC Scopus subject areas

  • Numerical Analysis
  • General Engineering
  • Applied Mathematics


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