Mathematics and Mechanics of Granular Materials

pp 167-184

Bifurcation analysis for shear localization in non-polar and micro-polar hypoplastic continua

  • Wenxiong HuangAffiliated withSchool of Engineering, The University of Newcastle
  • , Mohammed HjiajAffiliated withSchool of Engineering, The University of Newcastle
  • , Scott W. SloanAffiliated withSchool of Engineering, The University of Newcastle

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In this paper, shear localization in granular materials is studied as a bifurcation problem based on a conventional (non-polar) and a micro-polar continuum description. General bifurcation conditions are formulated for a non-polar hypoplastic model and its micro-polar continuum extension. These conditions stress, couple stress and density states at which weak discontinuity bifurcation may occur. The stress states for bifurcation are then compared with the peak stress states, which define a bounding surface for the accessible stress domain in the principal stress space. The results show that, in a micro-polar continuum description, the constitutive model may no longer be associated with weak discontinuity bifurcation.

Key words

bifurcation analysis granular materials hypoplasticity micro-polar continuum non-polar continuum