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

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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.