Assessing continuum postulates in simulations of granular flow

Rycroft, Chris H.; Kamrin, Ken; Bazant, Martin Z.

doi:10.1016/j.jmps.2009.01.009

Cited by 73 publications

(79 citation statements)

References 59 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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…”

Section: Summary Of the Modelmentioning

confidence: 99%

A finite element implementation of the nonlocal granular rheology

Henann¹,

Kamrin²

2016

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

SUMMARYInhomogeneous flows involving dense particulate media display clear size effects, in which the particle length scale has an important effect on flow fields. Hence, nonlocal constitutive relations must be used in order to predict these flows. Recently, a class of nonlocal fluidity models have been developed for emulsions and subsequently adapted to granular materials. These models have successfully provided a quantitative description of experimental flows in many different flow configurations. In this work, we present a finiteelement-based numerical approach for solving the nonlocal constitutive equations for granular materials, which involve an additional, non-standard nodal degree-of-freedom -the granular fluidity, which is a scalar state parameter describing the susceptibility of a granular element to flow. Our implementation is applied to three canonical inhomogeneous flow configurations: (i) linear shear with gravity, (ii) annular shear flow without gravity, and (iii) annular shear flow with gravity. We verify our implementation, demonstrate convergence, and show that our results are mesh-independent.

show abstract

“…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…”

Section: Summary Of the Modelmentioning

confidence: 99%

A finite element implementation of the nonlocal granular rheology

Henann¹,

Kamrin²

2016

Numerical Meth Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Central to the model is a scalar state variable g, called the granular fluidity, which represents the susceptibility of a granular cluster to flow. Mathematically, it functions as a field variable that relates the load intensity µ to the consequent flow rateγ, i.e.,γ = gµ, so that the tensorial relation between the Cauchy stress and the strain rate iswhere we have made the common assumption that the strain-rate and deviatoric Cauchy stress tensors are codirectional [17,18,26], though this is an approximation [28,29]. In a local description of granular flow, the fluidity is constitutively given as a function of the stress, in a manner consistent with Bagnold scaling [30].…”

mentioning

confidence: 99%

“…We denote the symmetric strain-rate tensor aṡ γ ij = (1/2)(∂v i /∂x j + ∂v j /∂x i ) with v i the velocity vector and x i the spatial coordinate. We then assume that steady flow proceeds at constant volume so thatγ kk = 0 [17,18,26,27] and define the equivalent shear strain rate asγ = (2γ ijγij ) 1/2 . Next, we introduce the symmetric Cauchy stress σ ij and define the pressure P = −(1/3)σ kk , the stress deviator σ…”

mentioning

confidence: 99%

See 1 more Smart Citation

Continuum Modeling of Secondary Rheology in Dense Granular Materials

Henann

Kamrin

2014

Phys. Rev. Lett.

Self Cite

View full text Add to dashboard Cite

Recently, a new nonlocal granular rheology was successfully used to predict steady granular flows, including grain-size-dependent shear features, in a wide variety of flow configurations, including all variations of the split-bottom cell. A related problem in granular flow is that of mechanicallyinduced creep, in which shear deformation in one region of a granular medium fluidizes its entirety, including regions far from the sheared zone, effectively erasing the yield condition everywhere. This enables creep deformation when a force is applied in the nominally quiescent region through an intruder such as a cylindrical or spherical probe. We show that the nonlocal fluidity model is capable of capturing this phenomenology. Specifically, we explore creep of a circular intruder in a two-dimensional annular Couette cell and show that the model captures all salient features observed in experiments, including both the rate-independent nature of creep for sufficiently slow driving rates and the faster-than-linear increase in the creep speed with the force applied to the intruder.Cooperativity is a hallmark of quasi-static, dense granular deformation. At a microscopic level, deformation in granular materials takes place through the rearrangement of clusters of grains. These rearrangement events lead to long-range fluctuations, or agitations, that influence the behavior of nearby clusters, leading to macroscopic manifestations of cooperativity, which are quite varied. Most familiarly, the length-scales associated with velocity fields in dense granular flows depend crucially upon the grain size [1], with grain-size dependent shear band widths being observed in many geometries [2][3][4][5][6][7][8]. Other manifestations of cooperativity include the dependence of volumetric outflow rate on grain size in drainage flows [9,10] and the so-called H stop -effect, in which thin granular layers require greater tilt to flow down an inclined surface [11,12]. A more recently-observed example of cooperativity in dense granular flows is that of mechanicallyinduced creep [13][14][15], understood as follows. When an intruder, such as a sphere, rod, or vane, is placed in a dense granular material, one must apply a force to the intruder that exceeds a critical value in order to move it through the granular media. However, shear deformation far from the intruder enables it to move, or creep, through the granular media for any non-zero value of the applied force -even when this force is less than the critical value. That is to say, flow anywhere in a granular media erases the yield condition everywhere! These cooperative phenomena provide stringent tests for a continuum model of granular flow. Local approaches to continuum modeling of granular materials, such as granular rheology [16][17][18] or soil mechanics [19,20], which relate the stress at a point to the local strain, strain-rate, or locally evolved state variables, are not equipped to address size-dependent manifestations of cooperativity. Recently, we proposed a nonlocal rheology for ...

show abstract

“…While, as noted in [28], dilation in dense flow does occur, it is typically on the order of only a few percent and quickly reaches a steady value over large deformations. Moreover, relative density (or packing fraction) is not necessary for purposes of computing flow motion; hence, the approximation of plastic incompressibility should have negligible effect on the velocity field of a dense granular flow.…”

Section: Flow Rulementioning

confidence: 81%

PFEM-based modeling of industrial granular flows

et al. 2014

View full text Add to dashboard Cite

The potential of numerical methods for the solution and optimization of industrial granular flows problems is widely accepted by the industries of this field, the challenge being to promote effectively their industrial practice. In this paper, we attempt to make an exploratory step in this regard by using a numerical model based on continuous mechanics and on the so-called Particle Finite Element Method (PFEM). This goal is achieved by focusing two specific industrial applications in mining industry and pellet manufacturing: silo discharge and calculation of power draw in tumbling mills. Both examples are representative of variations on the granular material mechanical response -varying from a stagnant configuration to a flow condition. The silo discharge is validated using the experimental data, collected on a full-scale flat bottomed cylindrical silo. The simulation is conducted with the aim of characterizing and understanding the correlation between flow patterns and pressures for concentric discharges. In the second example, the potential of PFEM as a numerical tool to track the positions of the particles inside the drum is analyzed. Pressures and wall pressures distribution are also studied. The power draw is also computed and validated against experiments in which the power is plotted in terms of the rotational speed of the drum.

show abstract

Assessing continuum postulates in simulations of granular flow

Cited by 73 publications

References 59 publications

A finite element implementation of the nonlocal granular rheology

A finite element implementation of the nonlocal granular rheology

Continuum Modeling of Secondary Rheology in Dense Granular Materials

PFEM-based modeling of industrial granular flows

Contact Info

Product

Resources

About