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[Jan Stránský <question269063@xxxxxxxxxxxxxxxxxxxxx>]

Question #269063 on Yade changed:
https://answers.launchpad.net/yade/+question/269063

    Status: Open => Answered

Jan Stránský proposed the following answer:
Hi Alexander,


> 1) Define material with the following class....(CmpMat e.g.)
>

for elastic behavior, any material (able to transfer tension) is fine. No
problem here


> 2) To calibrate young and poisson values u should use following
> algorithm...
>

For elastic material, you want to fit 2 macroscopic constants, e.g. Young's
modulus and Poissons's ratio. The main conclusion from the paper:
- The Young's modulus is directly proportional to 'young' CpmMat
parameters, so it can be fit trivially.
- Poisson's ratio does depend on 'poisson' CpmMat parameter, but
nonlinearly, so you can run simulations with different values to see the
relationship. As it is 1 variable, the optimization is not so difficult.


> 1) Create spheres packing (number of spheres, their relative
> location...etc)
>

Well, this is mainly up to you :-) Depending on your purposes (geometry,
loading), you can use regular packing, or random one
- regular packing is fine from my point of view for regular geometries.
- irregular is usually random so you will not get constant results. Also
you should use large amount of particles to get realistic results (In the
limit of infinite number of particles, you would get perfect results :-).
Moreover the boundaries will not be smooth anymore
- you may consider using some different discrete approach, something like
Cusatis' lattice model. You have very regular interaction network, so you
can also solve one cell of the truss-like interaction network analytically
"by hand".


> 2) Apply predefined pressure with ... function
>

this way (prescribing force on each particle from boundary layer) is the
most realistic


> 3) Compute stresses like this...
>

probably the biggest problem is here :-) If your displacements corresponds
to macroscopic Young's modulus and Poisson's ratio, then they are correct.
The stress and strain is just some post-processing and approximation from
discrete forces and displacements, so perfect results are not expectable :-)

Two points here:
- apart from stress, plot also contact forces. You will see, that at the
boundary (parallel to force) layer, the forces are different. It is because
the interactions distribution is different than "in the middle" (same
interactions in parallel direction, but only half in perpendicular and
diagonal direction). So if you are happy with middle stresses and strains,
you are on the right way :-)
- you can also put lower force value for conrner particles, as the force is
transmitted by this nonstandard parallel boundary layer. Do not forget to
redistribute this jump to the "middle" forces to preserve total force value
:-) You can again try different "jump" values to see the response, and
choose the correct "jump" value. The same approach you would choose, if you
directly apply nodal forces on FEM mesh and you want to get constant
stress/strain..
- Stress is computed from interactions. The fixed boundary and boundary
with prescribed force has half parallel interactions, so (very rouhly) you
get half stress. See [1], you can also compute it analytically by hand :-)
- The more particles you use, the smaller would be this boundary effects on
the overall results
- finally, you can try lower value of unbalanced force

cheers
Jan

PS: @Bruno: there are also diagonal bonds, so the interaction network is
relatively dense and the isotropy is moreless ok

[1] https://yade-
dem.org/doc/yade.utils.html#yade._utils.bodyStressTensors

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