A rigid-plastic micromechanical modeling of a random packing of frictional particles

The mechanical behavior of a random package of rigid particles, in which interparticle contact forces follow the Coulomb friction law, is analyzed with the aim of establishing a link between the microscopic frictional behavior of contacts, the equilibrium of particles and the macroscopic plasticity of this material. The concepts of kinematically admissible displacements and statically admissible forces are extended to this mechanical system and under a rather general assumption on particles shapes, it is shown that in the macro stress space the yield surface of this material is a cone. Further, the initial plastic flow of this material is examined in two particular cases and it is shown that in case of frictionless convex particles the plastic macro strain is associated, while in case of frictional identical spherical particles only its deviatoric part is associated. Finally a micromechanical derivation of the constitutive inequality relating the friction and dilatancy coefficients is given.