Nonlinear elasto-plastic model for dense granular flow

Abstract

This work proposes a model for granular deformation that predicts the stress and velocity profiles in well-developed dense granular flows. Recent models for granular elasticity (Jiang and Liu 2003) and rate-sensitive fluid-like flow (Jop et al. 2006) are reformulated and combined into one universal elasto-plastic law, capable of predicting flowing regions and stagnant zones simultaneously in any arbitrary 3D flow geometry. The unification is performed by justifying and implementing a Kröner-Lee decomposition, with care taken to ensure certain continuum physical principles are necessarily upheld. The model is then numerically implemented in multiple geometries and results are compared to experiments and discrete simulations.

A finite element implementation of the nonlocal granular rheology

“…Indeed, similar µ-fields in the rate-dependent regime have been observed in calculations of annular shear flow using the local-only model (see Fig. 5(d) of [4]). Figure 6.…”

“…We also make the assumption that plastic flow proceeds at constant volume, so that J p = det F p = 1, J = J e , and tr L p = trD p = 0. This is a standard assumption in the modeling of steady granular flow [32,25,33,34,4,14,15] and provides considerable simplification. This is equivalent to assuming that the material is always in its "critical state" [35], and all transient plastic volumetric dilatation or compaction (which is an important aspect of granular deformation [36,37]) has subsided.…”

“…where we have made the common assumption of codirectionality [3,38,4,14,15] of the plastic stretching and Mandel stress tensors. Defining the equivalent shear plastic strain rate aṡ…”

“…The approach begins with a description of flow in steady, homogeneous simple shearing -the local inertial rheology [2,3,4]. Consider a dry granular system made up of hard, quasi-monodisperse, spherical grains with mean grain diameter d and grain material density ρ s .…”

A visco‐elasto‐plastic model for granular materials under simple shear conditions

“…To achieve this goal, several constitutive models have been proposed in the literature, as those based on either dimensional analyses [30,31,32] or granular solid hydrodynamics [33]. In contrast, the theoretical constitutive model hereafter presented, as in Johnson and Jackson [34,35], Savage [36], Louge [37], Lee and Huang [38], Berzi et al [39] and Vescovi et al [40], assumes a parallel scheme according to which the stress tensor is evaluated as the sum of two contributions: one "ratedependent" and another "rate-independent".…”