Finite element simulation of localization in granular materials by micropolar continuum approach

There are two different approaches in continuum mechanics: a continuum considered as solid state – classical continuum mechanics – or a continuum with the microstructure. In order to explain the influences of microstructures on the behavior of materials, higher order effects such as moments that reflect the grain geometry and kinematics (e.g. rotations) must be incorporated, which in turn lead to a basic asymmetry of shear stress and micropolar (or Cosserat) effects. Cosserat continuum incorporates the characteristic length that relates the couple stresses and micro-curvatures at the constitutive model. Finite Element solutions of localization analysis have been carried out in Cosserat continuum to investigate length scale-size effect on the overall behavior of granular materials. The formulations of Cosserat elastoplasticity have been implemented into the nonlinear commercial finite element code using the user defined element utility. The mesh dependency effect in FE solution is reduced. The numerical model was used to predict the load–displacement behavior of a shallow footing and failure behavior of a slope. A proper treatment of the localization phenomenon in granular materials has been observed and simulated in Finite Element analysis.