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

The mechanical behavior of a random packing 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. A Reference Volume Element (RVE) containing a very large number of particles is examined and, under a rather general assumption on the shapes of particles, it is shown that in the macro stress space the yield surface of this material is a cone. Further, linear displacement boundary conditions are prescribed on the RVE and the plastic macro strain of this material is examined. It is shown that in case of frictional particles the plastic macro strain cannot be associated, while it is associated in case of frictionless particles. Further, in the particular case of frictional identical spheres, it is shown that only the deviatoric component of plastic macro strain is associated. Finally, a micromechanical derivation of the constitutive inequality relating the friction and dilatancy coefficients is given.