Xiaoxing Liu

Numerical study of structural evolution in shear band

At elevated stress levels, the deformation of granular assemblies has the tendency to localize in narrow shear bands. Recent research efforts within the granular material community are focusing on the morphology of deformation patterns within the bands. Understanding of the deformation mechanisms is a prerequisite for the quantification of energy dissipation, hardening and softening in the post-localization range. Despite significant experimental research efforts, a clear understanding of the flow properties and constitutive behaviours within the shear band is still elusive. This could mainly be attributed to the fact that shear bands are thin objects, making a detailed characterization of the particles’ behaviour and their interactions within shear bands difficult. As a numerical method, the Discrete Element Method (DEM) has demonstrated its ability to address this problem, owing to its intrinsic characteristic of tracing particle behaviour. This paper presents the results of application of DEM to model two-dimensional, densely packed, cohesionless, polydisperse granular assemblies under simple shear. Meso-scale kinematical information such as displacement field is evaluated. Within the shear band, the deformation field displays a vortex-like structure, and such vortex structures are accompanied by strong pore space production within the shear band. Analysis of the history of force chains inside the localized shear zone reveals that the formation of vortex structures is related to the kinematical evolution of a cycle encompassing buildup, buckling and collapse of the force chains.

Orientation of shear bands for a rigid plastic frictional material in simple shear

The orientation of shear bands is investigated analytically and numerically for a rigid plastic frictional material in simple shear. The model is based on co-axial flow rule, incompressible deformations and a friction factor which depends on the strain history. Since we are focussing on geological timescales, the influence of elasticity is neglected. Firstly, a linear stability analysis is performed confirming Rices 1976 assertion [The localization of plastic deformation, in Proceedings of the 14th International Congress on Theoretical and Applied Mechanics, W.T. Koiter, ed., North Holland, Amsterdam, 1976, p.207] that, in the hardening regime, bifurcation is possible at every stage. Orientation of shear bands against the less compressive principal axis lies anywhere between the Roscoe and Coulomb angles, namely between π/4+ψ/2 and π/4 + ϕ/2, where ϕ and ψ are the mobilised angles of friction and dilatancy, respectively (in our study, we assume ψ = 0). The linear stability analysis leaves open the question of which orientation will actually emerge in a boundary value problem that consider all nonlinearities. This question is addressed in a finite element study of simple shear with periodic boundary conditions in the shear direction. Our simulations show temporary inclined shear bands in the hardening regime followed by a persistent horizontal shear band. A sensitivity study with respect to geometric and constitutive parameters indicates that the height of the sample controls the orientation of the inclined shear bands. Finally, we extend our analytical and numerical studies to Cosserat plasticity. It turns out that inclined shear bands are suppressed for large values of the internal length R (narrow bands). The case of a standard continuum is gradually recovered for small R (wide bands).

Two-fluid Modeling of Geldart A Particles in Gas-solid Bubbling Fluidized Bed: Assessment of Drag Models and Solid Viscosity Correlations

Abstract In this work the influences of solid viscosity and the way to scale-down traditional drag models on the predicted hydrodynamics of Geldart A particles in a lab-scale gas-solid bubbling fluidized bed are investigated. To evaluate the effects of drag models, the modified Gibilaro et al. drag model (constant correction factor) and the EMMS drag model (non-constant correction factor) are tested. And the influences of solid viscosity are assessed by considering the empirical model proposed by Gidaspow et al. (1997, Turbulence, Viscosity and Numerical Simulation of FCC Particles in CFB. Fluidization and Fluid-particle Systems, AIChE Annual Meeting, Los Angeles, 58–62) and the models based on kinetic theory of granular flow (KTGF) with or without frictional stress. The resulting hydrodynamics by incorporating the different combinations of the drag model and solid viscosity model into two-fluid model (TFM) simulations are compared with the experimental data of Zhu et al. (2008, Detailed Measurements of Flow Structure inside a Dense Gas-Solids Fluidized Bed.” Powder Technological 180:339–349). The simulation results show that the predicted hydrodynamics closely depends on the setting of solid viscosity. When solid viscosity is calculated from the empirical model of Gidaspow et al., both drag models can reasonably predict the radial solid concentration profiles and particle velocity profiles. When the KTGF viscosity model without frictional stress is adopted, the EMMS drag model significantly over-estimates the bed expansion, whereas the modified Gibilaro et al. drag model can still give acceptable radial solid concentration profiles but over-estimate particle upwards and downwards velocity. When KTGF viscosity model with frictional stress is chosen, both drag models predict the occurrence of slugging. At this time, the particle velocity profiles predicted by EMMS drag model are still in well agreement with the experimental data, but the bed expansion is under-estimated.

Radial Segregation Driven by Axial Migration

The mixing of binary particles in a short rotating drum has been studied by performing discrete element simulations. The modeled granular materials were made of particles with same size and density but different color. We observed that the binary granular system inevitably went through a transient radial segregation state before reaching the final homogeneous mixing state. Depending on the filling degree and rotating speed, there exist totally three types of transient segregation patterns. Analysis of the flow field shows that such transient radial segregating phenomena were induced by different axial transporting characteristics of material.