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.chare...@hmg.inpg.fr <mailto:bruno.chare...@hmg.inpg.fr>> 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 >> >> >> _______________________________________________ >> Mailing list: https://launchpad.net/~yade-dev >> <https://launchpad.net/%7Eyade-dev> >> Post to : yade-dev@lists.launchpad.net >> <mailto:yade-dev@lists.launchpad.net> >> Unsubscribe : https://launchpad.net/~yade-dev >> <https://launchpad.net/%7Eyade-dev> >> More help : https://help.launchpad.net/ListHelp >> >> >> _______________________________________________ >> Mailing list: https://launchpad.net/~yade-dev >> <https://launchpad.net/%7Eyade-dev> >> Post to : yade-dev@lists.launchpad.net >> <mailto:yade-dev@lists.launchpad.net> >> Unsubscribe : https://launchpad.net/~yade-dev >> <https://launchpad.net/%7Eyade-dev> >> More help : https://help.launchpad.net/ListHelp > > > _______________________________________________ > Mailing list: https://launchpad.net/~yade-dev > Post to : yade-dev@lists.launchpad.net > Unsubscribe : https://launchpad.net/~yade-dev > More help : https://help.launchpad.net/ListHelp -- _______________ 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 ________________
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