Shearing of a narrow granular layer with polar quantities

Tejchman, J.; Gudehus, G.

doi:10.1002/1096-9853(200101)25:1<1::aid-nag115>3.0.co;2-8

Cited by 99 publications

(85 citation statements)

References 41 publications

(39 reference statements)

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“…Here the flow becomes rate-independent and deformation may become localized in shear bands (Vardoulakis, Goldscheider & Gudehus 1978) whose width is dependent on the grain size. The soil mechanics community have developed many models for shear banding, including higher gradient theories (Vardoulakis & Aifantis 1991), Cosserat theories (Tejchman & Gudehus 2001) and Hypoplastic models (Wu et al 1996). Kamrin (2010) combined the µ(I)-rheology with Jiang & Liu's (2003) model for granular elasticity and was able to compute steady-state solutions for rough-walled chute flow and an annular Couette cell as well as time-dependent solutions for a flat-bottomed silo.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Well-posed and ill-posed behaviour of the -rheology for granular flow

et al. 2015

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In light of the successes of the Navier-Stokes equations in the study of fluid flows, similar continuum treatment of granular materials is a long-standing ambition. This is due to their wide-ranging applications in the pharmaceutical and engineering industries as well as to geophysical phenomena such as avalanches and landslides. Historically this has been attempted through modification of the dissipation terms in the momentum balance equations, effectively introducing pressure and strain-rate dependence into the viscosity. Originally, a popular model for this granular viscosity, the Coulomb rheology, proposed rate-independent plastic behaviour scaled by a constant friction coefficient µ. Unfortunately, the resultant equations are always ill-posed. Mathematically ill-posed problems suffer from unbounded growth of short-wavelength perturbations, which necessarily leads to grid-dependent numerical results that do not converge as the spatial resolution is enhanced. This is unrealistic as all physical systems are subject to noise and do not blow up catastrophically. It is therefore vital to seek well-posed equations to make realistic predictions. The recent µ(I)-rheology is a major step forward, which allows granular flows in chutes and shear cells to be predicted. This is achieved by introducing a dependence on the non-dimensional inertial number I in the friction coefficient µ. In this paper it is shown that the µ(I)-rheology is well-posed for intermediate values of I, but that it is ill-posed for both high and low inertial numbers. This result is not obvious from casual inspection of the equations, and suggests that additional physics, such as enduring force chains and binary collisions, becomes important in these limits. The theoretical results are validated numerically using two implicit schemes for non-Newtonian flows. In particular, it is shown explicitly that at a given resolution a standard numerical scheme used to compute steady-uniform Bagnold flow is stable in the well-posed region of parameter space, but is unstable to small perturbations, which grow exponentially quickly, in the ill-posed domain.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Well-posed and ill-posed behaviour of the -rheology for granular flow

et al. 2015

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“…In all calculations, 896 quadrilateral elements divided into 3584 triangular elements were used. To properly capture shear localization inside of the specimen, the size of the finite elements was smaller than five times of the mean grain diameter d 50 (Tejchman and Gudehus 2001). The quadrilateral elements composed of four diagonally crossed triangles were used to avoid volumetric locking due to volume changes.…”

Section: Fe-input Datamentioning

confidence: 99%

Boundary effects on behaviour of granular material during plane strain compression

Tejchman¹,

Wu²

2010

European Journal of Mechanics - A/Solids

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The paper investigates the boundary effect on the behaviour of granular materials during plane strain compression using finite element method. A micro-polar hypoplastic constitutive model was used. The numerical calculations were carried out with different initial densities and boundary conditions. The behaviour of initially dense, medium dense and loose sand specimen with very smooth or very rough horizontal boundary was investigated. The formation of shear zones gave rise to different global and local stress and strain. Comparisons of the mobilized internal friction, dilatancy and non-coaxiality between global and local quantities were made.

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“…For the numerical calculations, the following micro-polar hypoplastic constitutive equation are considered (Tejchman and Gudehus 2001):…”

Section: Micro-polar Hypoplastic Constitutive Modelmentioning

confidence: 99%

Modeling of textural anisotropy in granular materials with stochastic micro-polar hypoplasticity

Tejchman

Wu²

2007

International Journal of Non-Linear Mechanics

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The paper deals with a numerical analysis of the effect of textural anisotropy on the behaviour of cohesionless granular materials with consideration of shear localization. For a simulation of the mechanical behavior of a granular material during a monotonic deformation path, an isotropic micropolar hypoplastic constitutive model was used. To describe textural effects, spatially correlated random fields of the initial void ratio were subject to rotation against the horizontal axis. The 2D random fields were generated using a conditional rejection method. The results were compared with those obtained with an anisotropic micro-polar constitutive model for an uniform distribution of the initial void ratio. The calculations were carried out with a dense granular specimen during plane strain compression under constant lateral pressure.Key words: finite element method, granular material, micro-polar hypoplasticity, random field, shear zone, textural anisotropy A c c e p t e d m a n u s c r i p t 2

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Shearing of a narrow granular layer with polar quantities

Cited by 99 publications

References 41 publications

Well-posed and ill-posed behaviour of the -rheology for granular flow

Well-posed and ill-posed behaviour of the -rheology for granular flow

Boundary effects on behaviour of granular material during plane strain compression

Modeling of textural anisotropy in granular materials with stochastic micro-polar hypoplasticity

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