Recent Progress in Energetic Probablistic Scaling Laws for Quasi-Brittle Fracture

Zdeněk P. Bažant, Jia Liang Le

Research output: Chapter in Book/Report/Conference proceedingChapter


Rational determination of safety factors necessitates establishing the probability density function (pdf) of the structural strength. For perfectly ductile and perfectly brittle materials, the proper pdf’s of the nominal strength of structure are known to be Gaussian and Weibullian, respectively, and are invariable with structure size and geometry. However, for quasibrittle materials, many of which came recently to the forefront of attention, the pdf has recently been shown to depend on structure size and geometry, varying gradually from Gaussian pdf with a remote Weibull tail at small sizes to a fully Weibull pdf at large sizes. The recent results are reviewed, and then mathematically extended in two ways: (1) to a mathematical description of structural lifetime as a function of applied (time-invariable) nominal stress, and (2) to a mathematical description of the statistical parameters of the pdf of structural strength as a function of structure size and shape. Finally, recent experimental data are analyzed and applicability of the present theory is verified.

Original languageEnglish (US)
Title of host publicationIUTAM Bookseries
PublisherSpringer Science and Business Media B.V.
Number of pages10
StatePublished - 2009

Publication series

NameIUTAM Bookseries
ISSN (Print)1875-3507
ISSN (Electronic)1875-3493


  • cohesive fracture
  • extreme value statistics
  • Probabilistic mechanics
  • scaling
  • size effect
  • structural strength

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Automotive Engineering
  • Materials Science(all)
  • Aerospace Engineering
  • Acoustics and Ultrasonics
  • Mechanics of Materials
  • Mechanical Engineering


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