Is the cause of size effect on structural strength fractal or energetic-statistical?

Zdeněk P. Bažant*, Arash Yavari

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

104 Scopus citations


The size effect on structural strength is an important phenomenon with a very old history. Unfortunately, despite abundant experimental evidence, this phenomenon is still not taken into account in most specifications of the design codes for concrete structures, as well as the design practices for polymer composites, rock masses and timber. The main reason appears to be a controversy between two different theories of size effect, namely the theory based on energetic-statistical scaling and the theory based on ideas from fractal geometry. This paper aims to critically analyze these two theories, examine their hypotheses and point out the limitations, in order to help code-writing committees choose a rational basis for their work. The paper begins by reviewing the theory of energetic size effect and the efforts to explain the size effect by fractal geometry. The advantages and disadvantages in modeling the structural size effect by fractals are pointed out. Certain flaws in the fractal theory of size effect are illuminated and it is shown that various aspects of this theory lack a sound physical or mathematical basis, or both. The paper ends by recommending how engineering designers and code writers should take the size effect into account.

Original languageEnglish (US)
Pages (from-to)1-31
Number of pages31
JournalEngineering Fracture Mechanics
Issue number1
StatePublished - Jan 1 2005

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering

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