Analytical and geometrical representation of localization in granular materials

Attempts to understand the phenomenon of shear banding through mathematical analysis required exclusive use of the fundamental principles of mechanics. The feasibility of capturing localized deformation using analytical and numerical methods has been demonstrated by a number of investigators. However, most of the formulations have been developed to deal with classical continuum mechanics approaches. In order to describe correctly localization phenomena, a continuum model with microstructure or Cosserat continuum have been formulated and implemented. The main purpose of this paper is to describe and simulate the localization geometrically and analytically for both classical and Cosserat media. Similarities and differences of the two approaches will be summarized. The importance of description of kinematics and statics of soil media with microstructure has been investigated. The nonsymmetric Cosserat formulation has been implemented for analytical and geometrical localization analysis.