ABSTRACT
The dissipative nature of structure evolution in granular media prompts the origins of many of the distinctive behavioural characteristics observed in such materials. When frictional sliding occurs, due to Coulomb criterion, a non-smooth relation governs the local force and displacement at a contact and as such, the rate at which a particle is sliding may not be explicitly expressed as a function of applied forces. Hence, even though stress/force and strain/displacement relations are established through homogenization from microscopic to macroscopic level, the missing link between force/deformation at particle scale prevents the writing of a constitutive expression at macroscopic level. Accordingly, other consistency equations should be established for the granular assembly to account for this missing link. These extra relations are also required since the description of microstructural characteristics involves more parameters than those concerned at macroscopic scale. A conversion between these two scales can only be developed if enough equations, in addition to those available from homogenization method, are provided. This paper deals with the preservation of energy across the microand macro-scales as one of the consistency equations postulating that for an assembly of rigid particles in quasi-static regime, the external energy transmitted into the sample at its boundaries fully translate into internal dissipation at sliding contacts. Assuming the coaxiality between strain increments and stress, it is shown that if a plastic potential for such material were to exist, it would be derived from microstructural evolutions. In this study, the explicit form of such a plastic potential function for the 2D case has been formulated
and its validity has been investigated through Discrete Element simulation.
