Nonlocal smeared cracking model for concrete fracture

Zdenek P Bazant, Feng Bao Lin

Research output: Contribution to journalArticlepeer-review

148 Scopus citations


The classical smeared cracking model widely used in finite-element analysis of concrete and rock cannot describe the size effect experimentally observed in brittle failures and exhibits spurious mesh sensitivity with incorrect convergence to zero energy dissipation at failure. The crack band model circumvents these deficiencies but has limitations with respect to mesh refinement, shear locking on zig-zag crack bands, and directional bias of the mesh. It is shown that all of these problems can be avoided by a nonlocal generalization, in which the damage that characterizes strain softening is considered to be a function of the spatial average of the positive part of the maximum principal strain. Two alternatives are presented: (1) Smeared cracking whose direction is fixed when cracks start to form; and (2) smeared cracking whose orientation rotates with the maximum principal strain. Furthermore, fracture tests on specimens of various sizes are analyzed by finite elements. It is shown that the model correctly reproduces the experimentally observed size effect and agrees with Bažant's size effect law. Orthogonal and slanted meshes are shown to yield approximately the same cracking zones and propagation directions. The model is easily programmed and computationally more efficient than the corresponding local version.

Original languageEnglish (US)
Pages (from-to)2493-2510
Number of pages18
JournalJournal of Structural Engineering (United States)
Issue number11
StatePublished - Jan 1 1988

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Building and Construction
  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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