yade-dev team mailing list archive

[Bruno Chareyre <bruno.chareyre@xxxxxxxxxxx>]

Hi Vincent,

I didn't see the need to find a reference for contour integral of Cauchy
stress, since it is something classical in continuum mechanics courses.
The demonstration is in function's documentation.

I don't understand this in your paper :
"At this scale, a Cauchy stress in the sense of continuous media cannot
be defined."

Why?
>
> Another think: I believe we can not talk about "exact mean stress
> tensor" at the particle level since the local volume is not well
> definable.
>
It is exact under some assumptions :
1. static equilibrium
2. Contact point paradigm : contact forces are applied on "points" (i.e.
surfaces of negligible size)
3. the solid phase has a constant volume, or variations are negligible
(a classical assumption, verified experimentaly on sands, eventualy
wrong in other materials)
If a given problem don't have all three assumptions satisfied, it can't
be said "exact", I agree. For the problem presented in your paper, it
can be considered exact IMHO.

Cheers.

Bruno

> Vincent
>
> Le 17 janv. 2011 à 20:43, Anton Gladky a écrit :
>
>> Thanks, Bruno!
>>
>> I will have a look at this, but, please, do not delete the previous
>> function, it is used in VTKRecorder.
>>
>> Anton
>>
>>
>>
>> On Mon, Jan 17, 2011 at 6:44 PM, Bruno Chareyre
>> <bruno.chareyre@xxxxxxxxxxx <mailto:bruno.chareyre@xxxxxxxxxxx>> wrote:
>>
>>     X <x-msg://1071/#12d951324e8b01b3_>LatexIt! run report...
>>
>>     *** Found expression $$\sigma_{ij}^{macro}/compacity$$
>>     Image was already generated
>>     *** Found expression $$\int_V s_{ij}dV = \int_{S_V} x_i.s_{ij}.n_j.dS = \sum_kx_i^k.f_j^k$$
>>
>>     Hi,
>>
>>     I've been adding another definition of stress in particles (not
>>     adapted to periodic BCs yet, though not difficult).
>>     For those interested. The documentation is pasted below.
>>     _____________
>>     Compute the exact mean stress tensor in each sphere from the
>>     contour integral of applied load.
>>     After divergence theorem, at equilibrium:
>>     <tblatex-11.png>.
>>     This relation applies for arbitrary shapes but the result has to
>>     be divided by the solid's volume, computed here using the radii,
>>     hence assuming spheres. The (weighted) average of per-body
>>     stresses is exactly equal to the average stress in the solid
>>     phase, i.e. <tblatex-8.png>.
>>     _____________
>>
>>     Cheers.
>>
>>     Bruno
>>
>>
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-- 
_______________
Bruno Chareyre
Associate Professor
ENSE³ - Grenoble INP
Lab. 3SR
BP 53 - 38041, Grenoble cedex 9 - France
Tél : +33 4 56 52 86 21
Fax : +33 4 76 82 70 43
________________