Size effect on structural strength: A review

Zdenek P Bazant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

268 Scopus citations


The article attempts a broad review of the problem of size effect or scaling of failure, which has recently come to the forefront of attention because of its importance for concrete and geotechnical engineering, geomechanics, arctic ice engineering, as well as for designing large load-bearing parts made of advanced ceramics and composites, e.g. for aircraft or ships. First, the main results of Weibull statistical theory of random strength are briefly summarized, and its applicability and limitations described. In this theory as well as plasticity, elasticity with a strength limit, and linear elastic fracture mechanics (LEFM), the size effect is a simple power law, because no characteristic size or length is present. Attention is then focused on the deterministic size effect in quasibrittle materials which, because of the existence of a non-negligible material length characterizing the size of the fracture process zone, represents the bridging between the simple power-law size effects of plasticity and of LEFM. The energetic theory of quasibrittle size effect in the bridging region is explained, and then a host of recent refinements, extensions and ramifications are discussed. Comments on other types of size effect, including that which might be associated with the fractal geometry of fracture, are also made. The historical development of the size-effect theories is outlined, and the recent trends of research are emphasized.

Original languageEnglish (US)
Pages (from-to)703-725
Number of pages23
JournalArchive of Applied Mechanics
Issue number9-10
StatePublished - Jan 1 1999


  • Asymptotic methods
  • Fracture mechanics
  • Quasibrittle materials
  • Scaling
  • Size effect

ASJC Scopus subject areas

  • Mechanical Engineering

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