Diffuse mode bifurcation of soil causing convection-like shear investigated by group-theoretic image analysis

Kiyohiro Ikeda, Hironori Sasaki, Tsuyoshi Ichimura

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Diffuse mode bifurcation of soil under plane-strain compression test is shown, by means of an image analysis based on group-theoretic bifurcation theory, to trigger convection-like shear and to precede shear band formation. First digital photos of Toyoura sand specimens are processed by PIV (particle image velocimetry) to gather digitized images of deformation. Next bifurcation from a uniform state is detected by expanding these images into the double Fourier series and finding a predominant harmonic diffuse bifurcation mode based on that theory. This harmonic bifurcation mode, which is the mixture of a few harmonic functions, expresses complex convection-like shear. Last bifurcation from a non-uniform state is detected by decomposing each image into a few images with different symmetries to extract non-harmonic diffuse bifurcation modes. Diffuse modes of bifurcation, which hitherto were hidden behind predominant uniform compressive deformation, have thus been made transparent by virtue of the group-theoretic image analysis proposed. A possible course of deformation suggested herein is the evolution of diffuse mode bifurcation with a convection-like bifurcation mode breaking uniformity and symmetry, followed by the formation of shear bands through localization.

Original languageEnglish
Pages (from-to)310-339
Number of pages30
JournalJournal of the Mechanics and Physics of Solids
Issue number2
Publication statusPublished - 2006 Feb 1


  • Bifurcation
  • Diffuse mode
  • Double Fourier series
  • Image analysis
  • Plane-strain compression test
  • Sand
  • Shear band

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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