Parametric hypoplasticity as continuum model for granular media: from Stokesium to Mohr-Coulombium and beyond

Fluid-particle systems, in which internal forces arise only from viscosity or intergranular friction, represent an important special case of strictly dissipative materials defined by a history-dependent 4th-rank viscosity tensor. In a recently proposed simplification, this history dependence is represented by a symmetric 2nd-rank fabric tensor with evolution determined by a given homogeneous deformation. That work suggests an essential physical link between idealized suspensions (“Stokesium”) and granular media (“Mohr-Coulombium”) along with possible models for the visco-plasticity of fluid-saturated and dry granular media. The present paper deals with the elastoplasticity of dilatant non-cohesive granular media composed of nearly rigid, frictional particles. Based on the underlying physics and past modeling by others, a continuum model based on parametric hypoplasticity is proposed, which involves a set of rate-independent ODEs in the state-space of stress, void ratio and fabric. As with the standard theory of hypoplasticity, the present model does not rely on plastic potentials but, in contrast to that theory, it is based explicitly on positive-definite elastic and plastic moduli. The present model allows for elastic loading or unloading within a dissipative yield surface and also provides a systematic treatment of Reynolds dilatancy as a kinematic constraint. Some explicit forms are proposed and comparisons are made to previous hypoplastic models of granular media.