Size effect

Zdeněk P. Bažant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

210 Scopus citations


This paper surveys the available results on the size effect on the nominal strength of structures - a fundamental problem of considerable importance to concrete structures, geotechnical structures, geomechanics, arctic ice engineering, composite materials, etc., with applications ranging from structural engineering to the design of ships and aircraft. The history of the ideas on the size effect is briefly outlined and recent research directions are emphasized. First, the classical statistical theory of size effect due to randomness of strength, completed by Weibull, is reviewed and its limitations pointed out. Subsequently, the energetic size effect, caused by stress redistributions due to large fractures, is discussed. Attention is then focused on the bridging between the theory of plasticity, which implies no size effect and is applicable for quasibrittle materials only on a sufficiently small scale, and the theory of linear elastic fracture mechanics, which exhibits the strongest possible deterministic size effect and is applicable for these materials on sufficiently large scales. The main ideas of the recently developed theory for the size effect in the bridging range are sketched. Only selected references to the vast amount of work that has recently been appearing in the literature are given.

Original languageEnglish (US)
Pages (from-to)69-80
Number of pages12
JournalInternational Journal of Solids and Structures
Issue number1-2
StatePublished - Jan 2000

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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