Localization-induced band and cohesive model

S. Hao, W. K. Liu*, D. Qian

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


A localization-induced cohesive model has been proposed for shear band evolution, crack growth, and fracture. Strain gradient theory has been applied to establish the criterion of the onset of localization and the governing equation in the post-bifurcation stage. Ana- lytical solutions in one-dimensional case are used to establish the “traction-separation” law, in which strain gradient and material intrinsic length scale present strong effects. In addition, the solution predicts a finite width for the localization-induced band. It is ob- served that a larger length scale contributes to the growth of a larger width of localization region and separation for softening materials. Hie proposed model provides a procedure to establish the fracture toughness analytically since the material length scale is taken into account. From the traction-separation analysis, it is found that damage de- creases separation, whereas an increase in material length scale increases the opening displacement; however, the traction-normalized opening displacement curves (with re- spect to the material length scale) are identical. Based on the methodology of multiple scale analysis in meshfree method, a computational approach has been proposed to enrich the one-dimensional traction-separation law to define fracture.

Original languageEnglish (US)
Pages (from-to)803-812
Number of pages10
JournalJournal of Applied Mechanics, Transactions ASME
Issue number4
StatePublished - Dec 2000

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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