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[Fu zuoguang <question254339@xxxxxxxxxxxxxxxxxxxxx>]

Question #254339 on Yade changed:
https://answers.launchpad.net/yade/+question/254339

Description changed to:
Dear Prof. Chareyre and all users:

  Thanks for helping me last time and today my questions are just about
the flexible boundary in Yade.

  The deformations within soils in plane strain state are commonly
concentrated in narrow zones called shear bands. These can be determined
as a significant representation of material instability and progressive
failure. After employing the local moment law to apply the rolling
resistance in each contact of pair of particles, I have run some
simulations to test the formation and evaluation of shear bands in Yade,
but just get some not so good results.

The attributes of shear bands depend on both the material properties,
such as particle size, shape and initial density and loading condition,
such as loading path and rate, as well as boundary condition. I think
that an improper boundary treatment used in my tasks may probably lead
my results to failure.

  In most of experiments in plain strain condition, rubber membranes are commonly used in horizontal direction. In order to construct this type of boundary in simulation, a kind of flexible boundary was adopted firstly by J. P. BARDET(1991) in his 2D DEM simulation, and then was extended by M.R.KUHN(1995) to 3D simulation. In J. P. BARDET(1991), this flexible boundary was described as follow (Fig.1):
‘The left and right boundaries are stress controlled, or flexible boundaries. Such a boundary is made of straight segments connecting the centers of external particles. Forces and moments are externally applied to the boundary particles by specifying the prescribed stress tensor.…..’

Lots of later achievements paying attention to shear bands in DEM
framework were used to employ this boundary as a necessary tool to
capture those narrow zones in their simulations. Both Oda (1999) and
Jiang (2010) got many of perfect results in their original purposes with
applying this flexible boundary. Fig.2 is the results of them. It is
obvious that there exists a bulge in each horizontal boundary as the end
point of shear band. This bulge is caused directly by deviatoric loading
and be intensely by the weak of horizontal constraints in this flexible
boundary. After the shear bands are relatively stable (inclination and
width cannot change any more), these two bulges can be then used to
measure the geometric attributes of the zones.

But now in Yade, I always used the rigid walls (aabb walls) as the only
type of boundary condition. This kind of rigid boundary made it a little
difficult to capture the narrow zones than what the flexible boundary
did. Fig.3 was my simulation results. Neither small number of particles
task nor large number can give me a clear description of the shear bands
and none of the two have no bulges in each horizontal boundaries. The
main reason, I think, is that the rigid boundaries used in the two
simulations bring an overly strict constraint in horizontal direction to
restrict the rotations of particles inside the shear bands.

Today my questions are:
[1] Are there something wrong in my descriptions of flexible boundary? If yes, please tell that.
[2] Can rigid walls be replaced by flexible boundary in Yade when I want to run 2D simulation? If yes, which example can help me for that purpose, if not, can you give me some suggestions on my 2D simulations.  

Seeking your help!

Fig 1 http://i1287.photobucket.com/albums/a628/fzgkkk/graph1_zpsfeea4d20.jpg
Fig 2 http://i1287.photobucket.com/albums/a628/fzgkkk/graph2_zps909c0847.jpg
Fig 3 http://i1287.photobucket.com/albums/a628/fzgkkk/grapl3_zps359307c0.jpg

Ref.
[1] A numerical investigation of the structure of persistent shear bands in granular media. 
[2] A flexible boundary for three-dimensional dem particle assemblies.
[3] Rolling resistance at contacts in simulation of shear band development by DEM.
[4] Modeling shear behavior and strain localization in cemented sands by two-dimensional distinct element method analyses

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