A continuum model for granular materials exhibiting a smooth transition between inelastic flow and elastic jamming

Abstract

A continuum model for granular materials, which transitions from an elastic jammed phase to rapid flows, is developed using a large deformation Eulerian formulation for compressible elastic-viscoplastic response. The model incorporates constitutive functions capturing μ(I) rheology, the value of the solid fraction developed for steady-state shearing, and the transient response for shear reversal based on experiments and simulations of interacting particles using the Discrete Element Method (DEM). The present model exhibits hyperelastic response with the stress determined by measures of elastic dilatation and elastic distortional deformations. This causes the stress to naturally have a direction different from the rate of deformation tensor for transient response. Examples examine pure dilation, steady-state simple shear, transient shearing with shear reversal for constant volume and constant non-shearing components of stress, and the transient transition to jamming.