Continuum modelling and simulation of granular flows through their many phases

Abstract

We propose and numerically implement a constitutive framework for granular media that allows the material to traverse through its many common phases during the flow process. When dense, the material is treated as a pressure sensitive elasto-viscoplastic solid obeying a yield criterion and a plastic flow rule given by the µ(I) inertial rheology of granular materials. When the free volume exceeds a critical level, the material is deemed to separate and is treated as disconnected, stress-free media. A Material Point Method (MPM) procedure is written for the simulation of this model and many demonstrations are provided in different geometries. By using the MPM framework, extremely large strains and nonlinear deformations, which are common in granular flows, are representable. The method is verified numerically and its physical predictions are validated against known results. BackgroundGranular materials present several modeling challenges when considering a continuum approach. During dense flow, the material can be characterized as an elasto-viscoplastic material with a frictional yield criterion. Extremely high levels of strain often occur, which challenge certain computational techniques, but the material can also behave as a solid, able to support shear loads in a static configuration. Moreover, because dry grains do not support tension, their constitutive behavior changes from that of a dense plastic media to a gas-like disconnected state during extension, a dramatic switch that is difficult to represent in a unified modeling and numerical framework.Several approaches have been used to simulate granular flow. One of the most accurate methods is the discrete element method (DEM), first described in Cundall & Strack (1979). While accurate, DEM solves the classical equations of motion on each grain individually, resulting in untenable computational expense over the large physical domains in many industrial and geological applications. A recent set of continuum rheological models for granular flow, such as the µ(I) relation in da Cruz et al. (2005) (later extended to 3D in Jop et al. (2006)) and the nonlocal extension in Kamrin & Koval (2012), offer a number of improvements over the commonly used rate-independent Drucker-Prager and Mohr-Coulomb models for problems with zones of dense, rapid flow (as is common in industrial settings) where rate-sensitivity is more pronounced and particle size-effects can play a role. The incompressible Navier-Stokes solver Gerris has been used in Staron et al. (2012) and Staron et al. (2014) with the µ(I) relation, while the commercial finite-element software Abaqus was used in Kamrin (2010) and appended with the nonlocal model in Henann & Kamrin (2013). While both methods can yield good results in certain regimes, the fluid solvers have difficulties with extensional disconnection and truly static zones cannot be represented, while the finite-element method (FEM) has issues when mesh distortion becomes large. Fixes such as Arbitrary-Lagrangian Eulerian (ALE) re-meshing may cause los...

The sands of time run faster near the end

“…The final surge comes either from the rapid decrease of the hydrostatic resistance ( R ∝ h ) or the mobilization of the grains. The latter is suggested by hopper simulations8 without interstitial medium. Direct observations of this phenomenon are not possible with the current setup.…”

Continuum Modeling of Pressure‐Balanced and Fluidized Granular Flows in 2‐D: Comparison With Glass Bead Experiments and Implications for Concentrated Pyroclastic Density Currents

“…This effect could be minimized by increasing the resolution in these regions (such as with adaptive gridding) or using numerical methods that better capture these concentration gradients. For example, models that treat the granular collapse by neglecting the gas phase often use other types of grids that deform: (1) the Material Point Method (Dunatunga & Kamrin, ), where information such as momentum, mass and stress are stored on material points that move as the flow advances; (2) the regularization method implemented with Taylor‐Hood finite elements for space discretization and an implicit Euler scheme with linearization for time discretization, which uses an Arbitrary Lagrangian Eulerian to deal with the displacement of the domain (Lusso et al, ).…”

“…This effect could be minimized by increasing the resolution in these regions (such as with adaptive gridding) or using numerical methods that better capture these concentration gradients. For example, models that treat the granular collapse by neglecting the gas phase often use other types of grids that deform: (1) the Material Point Method (Dunatunga & Kamrin, 2015), where information such as momentum, mass and stress are stored on material points that move as the flow advances;…”

“…In many settings, granular flows are neither steady and/or homogenous, and the inertial rheology, which depends locally on I does not reproduce observed dynamics. This is exemplified in cases with heterogeneous strain rate fields, where the yield criterion imposed by the material properties does not apply everywhere, as portions of the flow with μ < μ static remain flowing (Dunatunga & Kamrin, ). Additionally, Pouliquen () noted that thinner flows required higher slopes to come to rest, whereas the friction coefficient was thought to be equal the tangent of the slope angle irrespective of the flow thickness.…”

Intrusion rheology in grains and other flowable materials

“…Open states often occur temporarily in the wake of a moving intruder, before material from above collapses back down; see the Supplemental Materials (Section S1) for more details. An opening rule, while key to accurately representing many large flow processes in granular media, like the cases studied herein, is in fact a recently proposed modification in granular and soil plasticity (30), which traditionally restricts to dense, well-pressurized states. The bare-bones granular flow model we use does not account for ratesensitivity, strain-dependent strength/porosity, fabric anisotropy during flow, or nonlocal effects based on particle size, which are all known to exist.…”