On the stochastic interpretation of gradient-dependent constitutive equations

George Frantziskonis, Elias C. Aifantis

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


The paper elaborates on the statistical interpretation of a class of gradient models by resorting to both microscopic and macroscopic considerations. The microscopic stochastic representation of stress and strain fields reflects the heterogeneity inherently present in engineering materials at small scales. A physical argument is advanced to conjecture that stress shows small fluctuations and strong spatial correlations when compared to those of strain; then, a series expansion in the respective constitutive equations renders unimportant stress gradient terms, in contrast to strain gradient terms, which should be retained. Each higher-order strain gradient term is given a physically clear interpretation. The formulation also allows for the underlying microstrain field to be statistically non-stationary, e.g., of fractal character. The paper concludes with a comparison between surface effects predicted by gradient and stochastic formulations.

Original languageEnglish (US)
Pages (from-to)589-596
Number of pages8
JournalEuropean Journal of Mechanics, A/Solids
Issue number4
StatePublished - 2002


  • Constitutive relations
  • Gradients
  • Heterogeneity
  • Stochastic

ASJC Scopus subject areas

  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering
  • General Physics and Astronomy


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