On the rheology of dilative granular media: Bridging solid- and fluid-like behavior

Finite element continuum modeling of vibrationally-fluidized granular flows

“…The equivalent Young's modulus, E b , of quasistatic granular flows has been conventionally determined in triaxial compression tests either experimentally or numerically using DEM (Andrade et al, 2011(Andrade et al, , 2012Andrade and Tu, 2009). It is also possible to use the Mindlin theory to derive equations for sound wave propagation speed in the granular media assuming that the particles are always in contact and that force chains remain largely unchanged (Andrade et al, 2012). Therefore, for the present vibrationally-fluidized beds, these approaches give inaccurate values of the equivalent Young's modulus since the force chains change at every time step (Andrade et al, 2012).…”

“…Previous efforts to model granular flows using a continuum approach have focused on the bulk flow behavior of the nonfluidized granular media such as in the flow down inclined chutes (Kamrin, 2010;Jop et al, 2006;Andrade et al, 2012), plane shear flow (Midi, 2004;Cruz et al, 2005), flow in rotating drums (Forterre and Pouliquen, 2008;Midi, 2004), flow in annular shear cells (Kamrin, 2010;Forterre and Pouliquen, 2008;Midi, 2004), and silo discharge flows (Rycroft et al, 2009;Forterre and Pouliquen, 2008;Midi, 2004). In these cases of non-fluidized flows, constitutive equations were defined to describe the bulk flow of the granular materials under quasi-static and moderate flow (liquid-like) regions (Kamrin, 2010;Jop et al, 2006;Andrade et al, 2012). To the authors' knowledge, no papers have been published on continuum modeling of vibrationally-fluidized granular flows.…”

“…To the authors' knowledge, no papers have been published on continuum modeling of vibrationally-fluidized granular flows. The continuum models that have been used for quasi-static and moderate flow include different elasto-plastic formulations of the equivalent continuum media (Kamrin, 2010;Andrade et al, 2012;Andrade and Tu, 2009), and visco-plastic formulations considering only the plastic behavior of the equivalent media under time-varying shear deformation (Jop et al, 2006;Forterre and Pouliquen, 2008). In many cases, DEM was used to obtain the equivalent properties needed to model the granular flows as a continuum (Rycroft et al, 2009;Forterre and Pouliquen, 2008;Midi, 2004;Cruz et al, 2005;Andrade et al, 2011;Guo et al, 2012).…”

“…In many cases, DEM was used to obtain the equivalent properties needed to model the granular flows as a continuum (Rycroft et al, 2009;Forterre and Pouliquen, 2008;Midi, 2004;Cruz et al, 2005;Andrade et al, 2011;Guo et al, 2012). For example, the equivalent stress tensor, pressure and shear rate at different points of a flowing granular bed were obtained using DEM, and were then used to determine the equivalent continuum media elastic and plastic properties (Rycroft et al, 2009;Andrade et al, 2011Andrade et al, , 2012. Generally, the average streamlines, and hence the bulk flow behavior, determined through these continuum simulations have been in fairly good agreement with the predictions of discrete element modeling (Kamrin, 2010;Forterre and Pouliquen, 2008;Andrade et al, 2012).…”

“…For example, the equivalent stress tensor, pressure and shear rate at different points of a flowing granular bed were obtained using DEM, and were then used to determine the equivalent continuum media elastic and plastic properties (Rycroft et al, 2009;Andrade et al, 2011Andrade et al, , 2012. Generally, the average streamlines, and hence the bulk flow behavior, determined through these continuum simulations have been in fairly good agreement with the predictions of discrete element modeling (Kamrin, 2010;Forterre and Pouliquen, 2008;Andrade et al, 2012). For example, Kamrin (2010) proposed an elasto-plastic constitutive law for use in a Lagrangian finite element model of granular flows in inclined chutes, rectangular silos and annular Couette cells.…”