Simulation of strain localization with discrete element-Cosserat continuum finite element two scale method for granular materials

A multiscale method is proposed based on an individual particle provided with rotational freedom, which considers the kinematic connections and transformation consistency of physical parameters in micro-macro models, as well as the need for a regularization mechanism in the classical macroscopic continuum model to preserve the well-posedness of the localization problem. This method uses the discrete element method to incorporate both rolling resistances (rolling friction tangential force and rolling resistance moment) and the sliding friction tangential force between particles in the contact model on a microscopic scale, while the Cosserat continuum is used to describe the granular materials on a macroscopic scale. In addition, a consistent return mapping algorithm for the integration of the rate constitutive equation and the closed form of the consistent elastoplastic tangent modulus matrix for the generalized elastoplastic Cosserat continuum model are presented. The effectiveness of the developed multiscale method is demonstrated with two cases: one comparing discrete element computations with the Cosserat finite element analysis, and the other comparing a plane strain compression experiment using digital imaging measurements with the Cosserat finite element analysis. The rotational deformation and shear band failure modes are well reproduced in both cases. It also demonstrates that the present model has better performance in predicting the phenomena of shear bands than previous ones.