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 journalArticle

9 Scopus citations

Abstract

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
Volume20
Issue number6
DOIs
StatePublished - Nov 1 2001

Keywords

  • Fracture energy
  • Gradients
  • Strength
  • Wavelets

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

Fingerprint Dive into the research topics of 'Scale-dependent constitutive relations and the role of scale on nominal properties'. Together they form a unique fingerprint.

  • Cite this