Analysis of shear bands in slow granular flows using a frictional Cosserat model

2000 ◽  
Vol 627 ◽  
Author(s):  
Prabhu R. Nott ◽  
K. Kesava Rao ◽  
L. Srinivasa Mohan
Keyword(s):  
Scaling Laws ◽  
Shear Bands ◽  
Shear Layers ◽  
Theoretical Description ◽  
Field Variable ◽  
Cosserat Continuum ◽  
Momentum Balance ◽  
Rigid Plastic ◽  
Independent Field ◽  
Cosserat Model

ABSTRACTThe slow flow of granular materials is often marked by the existence of narrow shear layers, adjacent to large regions that suffer little or no deformation. This behaviour, in the regime where shear stress is generated primarily by the frictional interactions between grains, has so far eluded theoretical description. In this paper, we present a rigid-plastic frictional Cosserat model that captures thin shear layers by incorporating a microscopic length scale. We treat the granular medium as a Cosserat continuum, which allows the existence of localised couple stresses and, therefore, the possibility of an asymmetric stress tensor. In addition, the local rotation is an independent field variable and is not necessarily equal to the vorticity. The angular momentum balance, which is implicitly satisfied for a classical continuum, must now be solved in conjunction with the linear momentum balances. We extend the critical state model, used in soil plasticity, for a Cosserat continuum and obtain predictions for flow in plane and cylindrical Couette devices. The velocity profile predicted by our model is in qualitative agreement with available experimental data. In addition, our model can predict scaling laws for the shear layer thickness as a function of the Couette gap, which must be verified in future experiments. Most significantly, our model can determine the velocity field in viscometric flows, which classical plasticity-based model cannot.

scholarly journals A frictional Cosserat model for the slow shearing of granular materials

2002 ◽  
Vol 457 ◽  
pp. 377-409 ◽  
Author(s):  
L. SRINIVASA MOHAN ◽  
K. KESAVA RAO ◽  
PRABHU R. NOTT
Keyword(s):  
Angular Velocity ◽  
Granular Material ◽  
Shear Layer ◽  
Granular Materials ◽  
Layer Thickness ◽  
Couette Flow ◽  
Velocity Fields ◽  
Cosserat Continuum ◽  
Cosserat Model ◽  
Cylindrical Couette Flow

A rigid-plastic Cosserat model for slow frictional flow of granular materials, proposed by us in an earlier paper, has been used to analyse plane and cylindrical Couette flow. In this model, the hydrodynamic fields of a classical continuum are supplemented by the couple stress and the intrinsic angular velocity fields. The balance of angular momentum, which is satisfied implicitly in a classical continuum, must be enforced in a Cosserat continuum. As a result, the stress tensor could be asymmetric, and the angular velocity of a material point may differ from half the local vorticity. An important consequence of treating the granular medium as a Cosserat continuum is that it incorporates a material length scale in the model, which is absent in frictional models based on a classical continuum. Further, the Cosserat model allows determination of the velocity fields uniquely in viscometric flows, in contrast to classical frictional models. Experiments on viscometric flows of dense, slowly deforming granular materials indicate that shear is confined to a narrow region, usually a few grain diameters thick, while the remaining material is largely undeformed. This feature is captured by the present model, and the velocity profile predicted for cylindrical Couette flow is in good agreement with reported data. When the walls of the Couette cell are smoother than the granular material, the model predicts that the shear layer thickness is independent of the Couette gap H when the latter is large compared to the grain diameter dp. When the walls are of the same roughness as the granular material, the model predicts that the shear layer thickness varies as (H/dp)1/3 (in the limit H/dp [Gt ] 1) for plane shear under gravity and cylindrical Couette flow.

scholarly journals Non-trivial avalanches triggered by shear banding in compression of metallic glass foams

2020 ◽  
Vol 476 (2240) ◽  
pp. 20200186
Author(s):  
H. Lin ◽  
C. lu ◽  
H. Y. Wang ◽  
L. H. Dai
Keyword(s):  
Metallic Glass ◽  
Scaling Laws ◽  
Waiting Times ◽  
Shear Banding ◽  
Shear Bands ◽  
Mean Field ◽  
Structural Disorder ◽  
Aftershock Sequence ◽  
Atomic Scale ◽  
Characteristic Time Scale

Ductile metallic glass foams (DMGFs) are a new type of structural material with a perfect combination of high strength and toughness. Owing to their disordered atomic-scale microstructures and randomly distributed macroscopic voids, the compressive deformation of DMGFs proceeds through multiple nanoscale shear bands accompanied by local fracture of cellular structures, which induces avalanche-like intermittences in stress–strain curves. In this paper, we present a statistical analysis, including distributions of avalanche size, energy dissipation, waiting times and aftershock sequence, on such a complex dynamic process, which is dominated by shear banding. After eliminating the influence of structural disorder, we demonstrate that, in contrast to the mean-field results of their brittle counterparts, scaling laws in DMGFs are characterized by different exponents. It is shown that the occurrence of non-trivial scaling behaviours is attributed to the localized plastic yielding, which effectively prevents the system from building up a long-range correlation. This accounts for the high structural stability and energy absorption performance of DMGFs. Furthermore, our results suggest that such shear banding dynamics introduce an additional characteristic time scale, which leads to a universal gamma distribution of waiting times.

A Coupled Model of Two-Phase Diffusion and Flow through Deforming Porous Cosserat Media

2010 ◽  
Vol 297-301 ◽  
pp. 281-293 ◽  
Author(s):  
Deepak P. Adhikary ◽  
Hua Guo
Keyword(s):  
Porous Medium ◽  
Continuum Theory ◽  
Cosserat Continuum ◽  
Rock Deformation ◽  
Two Phase ◽  
Bedding Planes ◽  
Permeability Changes ◽  
Cosserat Model ◽  
Cosserat Continuum Theory ◽  
Fluid Diffusion

Simulation of mining induced rock deformation, rock fracture enhanced permeability and fluid and gas diffusion and flow process is a complex task. A new three dimensional coupled mechanical two-phase double porosity desorption and diffusion finite element code called COSFLOW has been recently developed by CSIRO Exploration and Mining to service the mining industry’s need. A unique feature of COSFLOW is the incorporation of Cosserat continuum theory in its formulation. In the Cosserat model, inter-layer interfaces (joints, bedding planes) are considered to be smeared across the mass, i.e. the effects of interfaces are incorporated implicitly in the choice of stress-strain model formulation. An important feature of the Cosserat model is that it incorporates bending rigidity of individual layers in its formulation and this makes it different from other conventional implicit models. The Cosserat continuum formulation has a major advantage over conventional continuum models in that it can efficiently simulate rock breakage and slip as well as separation along the bedding planes. Any opening/closure along a bedding plane may introduce a strong anisotropy in fluid flow properties of the porous medium. This, in turn, will impact on the fluid/gas flow behaviour of the porous medium. This paper will briefly describe the Cosserat continuum theory, the treatment of permeability changes with rock deformation and the coupling of the two-phase dual porosity fluid diffusion- flow model and present a number of examples highlighting the capability of the developed code in simulating the mining induced rock deformation, permeability changes and fluid diffusion and flow will be presented.

Dynamic Patterning of Shear Bands in Cosserat Continuum

1997 ◽  
Vol 123 (2) ◽  
pp. 123-133 ◽  
Author(s):  
J. Tejchman ◽  
W. Wu
Keyword(s):  
Shear Bands ◽  
Cosserat Continuum

Numerical study on patterning of shear bands in a Cosserat continuum

1993 ◽  
Vol 99 (1-4) ◽  
pp. 61-74 ◽  
Author(s):  
J. Tejchman ◽  
W. Wu
Keyword(s):  
Numerical Study ◽  
Shear Bands ◽  
Cosserat Continuum

On adiabatic shear bands in rigid-plastic materials

1989 ◽  
Vol 78 (3-4) ◽  
pp. 263-279 ◽  
Author(s):  
B. D. Coleman ◽  
D. C. Newman
Keyword(s):  
Shear Bands ◽  
Adiabatic Shear ◽  
Adiabatic Shear Bands ◽  
Rigid Plastic ◽  
Plastic Materials

On the Scaling of Low-Velocity Perforation of Mild Steel Plates

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
Norman Jones ◽  
R. S. Birch
Keyword(s):  
Mild Steel ◽  
Scaling Laws ◽  
Experimental Results ◽  
Steel Plates ◽  
Ductile Deformation ◽  
Low Velocity ◽  
Rigid Plastic ◽  
Scale Range ◽  
Simple Equations ◽  
The Impact

Experimental results are reported for the perforation of geometrically similar fully clamped circular and square mild steel plates struck transversely by cylindrical projectiles having blunt, conical, and hemispherical noses. The striking masses are much heavier than the corresponding plate mass and travel with initial impact velocities up to about 12m∕s. The blunt projectiles perforate the plating easiest, while the hemispherical-nosed ones require the greatest energy. The perforation energy of a conical-nosed projectile is somewhat less than that for a hemispherical-nosed one. The data are used to explore the validity of the geometrically similar scaling laws over a geometric scale range of 4. The experimental results are compared to the empirical equations for the impact perforation of plates and with theoretical rigid-plastic predictions for the large ductile deformation behavior of those test specimens, which did not suffer cracking or perforation. The experimental results satisfy the requirements of geometrically similar scaling and some simple equations are presented, which are useful for design purposes.

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