A unified formulation for plasticity models of granular and other materials

Abstract

A general physically based rule for the kinematics of planar deformation of granular materials is presented and a pair of kinematic equations governing the velocity field is obtained. The method results in a unified derivation of the equations for the double sliding, free rotating model, the double shearing model and the plastic potential model for granular materials. The formulation of the double sliding, free rotating model for the kinematics of granular materials presented here is consistent with the continuum theory of constitutive equations and demonstrates the relationship of this model both to the double shearing model and to the plastic potential models. Expressions for the rate of working of the stresses are presented. A constitutive equation, expressed in terms of planar tensor quantities, is also presented that has the three models as special cases.