Nonlocal microplane model for fracture, damage, and size effect in structures

Zdeněk P. Bažant, Joško Ožbolt

Research output: Contribution to journalArticlepeer-review

190 Scopus citations


A generalized microplane model, which was previously developed to describe tensile cracking and nonlinear triaxial response of brittle-plastic materials in compression and shear, is implemented in a finite element code. To limit localization instabilities due to strain softening and the consequent spurious meshsensitivity, the recently proposed concept of nonlocal continuum with local strain (nonlocal damage) is adopted and combined with the microplane model. An effective numerical algorithm permitting large loading steps is developed by applying the idea of exponential algorithms previously used for creep. Problems due to nonsymmetry of the tangential stiffness matrix are avoided by using the initial elastic stiffness matrix in the incremental force-displacement relations. Numerical results demonstrate that the microplane model, which previously has allowed an excellent description of the test data on nonlinear triaxial behavior of concrete as well as unidirectional and multidirectional crack or crack shear, is endowed (in its nonlocal generalization) with the capability of also modeling tensile fracture. The model yields the correct transitional size effect observed in concrete and agrees with the recently proposed size effect law. The formulation is applicable to brittle-plastic materials in general.

Original languageEnglish (US)
Pages (from-to)2485-2505
Number of pages21
JournalJournal of Engineering Mechanics
Issue number11
StatePublished - Nov 1990

ASJC Scopus subject areas

  • Mechanics of Materials
  • Mechanical Engineering


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