A UNIFIED FORMULATION FOR PLASTICITY MODELS OF GRANULAR AND OTHER MATERIALS

A general physically based rule for the kinematics of planar deformati on of granular materials is presented and a pair of kinematic equation s governing the velocity field is obtained. The method results in a un ified derivation of the equations for the double sliding, free rotatin g model, the double shearing model and the plastic potential model for granular materials. The formulation of the double sliding, free rotat ing model for the kinematics of granular materials presented here is c onsistent with the continuum theory of constitutive equations and demo nstrates the relationship of this model both to the double shearing mo del and to the plastic potential models. Expressions for the rate of w orking of the stresses are presented. A constitutive equation, express ed in terms of planar tenser quantities, is also presented that has th e three models as special cases.