Localization and Bifurcation Analysis of Granular Materials in Micropolar Continuum

The onset of strain localization is indicated by the weak-discontinuity bifurcation condition-namely, the determinant of the acoustic tensor must be zero. In this study, the analytical solution of the acoustic tensors in plane-strain condition was derived for both the Cauchy-Boltzmann continuum and the micropolar continuum. A typical elastoplastic constitutive model based on the Drucker-Prager criterion was implemented in Abaqus by utilizing its user-defined material (UMAT) and user-defined element (UEL) options. The validity of the localization condition was verified and compared for the Cauchy-Boltzmann continuum and the micropolar continuum through the plane-strain numerical experiments. Results showed that the determinant of the acoustic tensor in the micropolar continuum tended to a constant value when the localization occurred rather than tending to zero as in the Cauchy-Boltzmann continuum. This indicates that the micropolar continuum can prevent the ill-posed solution when bifurcation occurs; in contrast, the onset of localization in the micropolar continuum is totally the same as that in the Cauchy-Boltzmann continuum.