Strain localization is a well-known phenomenon, generally associated with plastic deformation and rupture in solids, especially in granular materials. During localization, deformation is observed to concentrate in narrow zones called shear bands. Shear bands and ruptures control the overall pattern of behavior of a particulate material such as a soil mass in a variety of engineering situations.; Gradient plasticity formulations are presented to model localized deformation in granular materials. The first formulation incorporates the gradient of effective plastic strain into the pressure dependent yield surface in an elasto-plastic model. Since at the microscale shearing occurs along several active planes through sliding and rolling of grains over each other at active contacts, a multi-slip crystal plasticity formulation is proposed next to develop a micromechanics based model to study the localization phenomenon. The effect of heterogeneity and anisotropy within the multi-slip formulation is accounted for directly by assuming the mobilized friction in the pressure dependent yield surface formulation to be a direct function either of the gradient of the porosity distribution or of the fabric tensor, respectively. The first formulation and a double slip version of multi slip formulation have been implemented into a finite element code and used to simulate biaxial shear tests on dry sand.; Based on the analyses conducted using the first formulation, it is shown that the shape of the post peak segment of the load displacement curve predicted by the numerical analysis is dependent on the finite element mesh size when gradient term is not used. The gradient is found to diffuse the concentration of plastic strains within the shear band resulting in a consistent width regardless of the mesh refinement.; Based on the analyses conducted using the double slip formulation it is shown that shear band orientation is a function of the initial slip system within a granular material. Initial fabric was found to influence the initiation, location, and the inclination of the shear band. The double slip formulation was able to capture the dip in the vertical stress distribution at the base of a granular pile observed experimentally by physicists.
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