Scale-dependent constitutive relations and the role of scale on nominal properties

George N. Frantziskonis, Avraam A. Konstantinidis, Elias C. Aifantis

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


Size effects in strength and fracture energy of heterogeneous materials is considered within a context of scale-dependent constitutive relations. Using tools of wavelet analysis, and considering the failure state of a one-dimensional solid, constitutive relations which include scale as a parameter are derived from a 'background' gradient formulation. In the resulting theory, scale is not a fixed quantity independent of deformation, but rather directly dependent on the global deformation field. It is shown that strength or peak nominal stress (maximum point at the engineering stress-strain diagram) decreases with specimen size while toughness or total work to fracture per nominal area (area under the curve in the engineering stress-strain diagram integrated along the length of the considered one-dimensional specimen) increases. This behavior is in agreement with relevant experimental findings on heterogeneous materials where the overall mechanical response is determined by variations in local material properties. The scale-dependent constitutive relations are calibrated from experimental data on concrete specimens.

Original languageEnglish (US)
Pages (from-to)925-936
Number of pages12
JournalEuropean Journal of Mechanics, A/Solids
Issue number6
StatePublished - Nov 2001


  • Fracture energy
  • Gradients
  • Strength
  • Wavelets

ASJC Scopus subject areas

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


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