Simulation and interpretation of diffuse mode bifurcation of elastoplastic solids

Kiyohiro Ikeda, Yuki Yamakawa, Seiichiro Tsutsumi

Research output: Contribution to journalArticlepeer-review

25 Citations (Scopus)


The diffuse mode bifurcation of elastoplastic solids at finite strain is investigated. The multiplicative decomposition of deformation gradient and the hyperelasto-plastic constitutive relationship are adapted to the numerical bifurcation analysis of the elastoplastic solids. First, bifurcation analyses of rectangular plane strain specimens subjected to uniaxial compression are conducted. The onset of the diffuse mode bifurcations from a homogeneous state is detected; moreover, the post-bifurcation states for these modes are traced to arrive at localization to narrow band zones, which look like shear bands. The occurrence of diffuse mode bifurcation, followed by localization, is advanced as a possible mechanism to create complex deformation and localization patterns, such as shear bands. These computational diffuse modes and localization zones are shown to be in good agreement with the associated experimental ones observed for sand specimens to ensure the validity of this mechanism. Next, the degradation of horizontal sway stiffness of a rectangular specimen due to plane strain uniaxial compression is pointed out as a cause of the bifurcation of the first antisymmetric diffuse mode, which triggers the tilting of the specimen. Last, circular and punching failures of a footing on a foundation are simulated.

Original languageEnglish
Pages (from-to)1649-1673
Number of pages25
JournalJournal of the Mechanics and Physics of Solids
Issue number9
Publication statusPublished - 2003 Sep 1


  • B. Elastic-plastic material
  • B. Finite strain
  • C. Finite elements
  • C. Stability and bifurcation

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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