yade-dev team mailing list archive

[Chiara Modenese <c.modenese@xxxxxxxxx>]

Oh thanks Bruno! I will see how it works. Perhaps we do not really need a
precise determination, this could be sufficient. Will try.

For time step determination of elastic bodies (so no damping), I think I
will also add a formulation based on the Rayleigh wave speed propagation
which Thornton uses for his elasto-plastic adhesive particles (he does not
use viscous damping, but particles can deform plastically).

cheers, Chiara


On 28 February 2011 08:31, Bruno Chareyre <bruno.chareyre@xxxxxxxxxxx>wrote:

>  This idea seems to work well. The integration is always stable with safety
> factors 0.8 on both dt_e and dt_v (I made a mistake on dt_v which must be
> less than 2A/B, not 2B/A), and dt=min(0.8*dt_e,0.8*dt_v).
> See attached speadsheet.
>
> Bruno
>
>
>
> On 25/02/11 21:24, Bruno Chareyre wrote:
>
> X <#12e6b6340ff11f30_>LatexIt! run report...
>
> *** Found expression $$dt_e,dt_v$$
> Image was already generated
> *** Found expression $$dt_e$$
> Image was already generated
> *** Found expression $$dt_v<2b/a$$
> Image was already generated
> *** Found expression $$\dot{X} = (1 - dt.a/b)\dot{X}$$
> *** Found expression $$\dot{X}_{t+dt} = \dot{X}_{t}-dt.a/b.\dot{X}_{t}$$
> Image was already generated
> *** Found expression $$a\ddot{X}+b\dot{X}+X=0$$
> Image was already generated
>
>  better with LatexIt, sorry.
>
> A lazy time-step determination :
>
> I recall the problem we solve is:[image: $$a\ddot{X}+b\dot{X}+X=0$$]
>
> 1/ If the viscous effects "b" are high compared to elastic effects, then
> it means b>>1 and the "X" term can be neglected.
> In that case a first order(*) explicit scheme will give[image: $$\dot{X}_{t+dt} = \dot{X}_{t}-dt.a/b.\dot{X}_{t}$$]
> or[image: $$\dot{X} = (1 - dt.a/b)\dot{X}$$]
> which obviously converges only if [image: $$dt_v<2b/a$$].
> In the absence of a better derivation, this condition should at least be
> verified for all visco-simulation.
>
> (*) If the current implementation uses previous velocity to determine
> the viscous force, then it is first order scheme. Is it the case?
>
> 2/ If viscous effects are small in comparison with stiffness (highly
> "under-relaxed", if you like), then the elastic times-step [image: $$dt_e$$]
> given by GSTStepper is a good enough approximate.
>
> 3/ If nothing can be neglected, then there a critical timestep smaller
> than the two timesteps defined above, this is the interesting but
> difficult part.
> It could be workarounded, maybe, by defining a sufficiently small safety
> factor, like dt=0.5*min([image: $$dt_e,dt_v$$]). It would need numerical
> experiments to see if this method applies.
>
> I examined the true visco-elastic problem today and found a big equation
> giving a conditon on dt, but I couldn't solve it by hand yet... :-(
>
> 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
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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
> ________________
>
>
> _______________________________________________
> Mailing list: https://launchpad.net/~yade-dev
> Post to     : yade-dev@xxxxxxxxxxxxxxxxxxx
> Unsubscribe : https://launchpad.net/~yade-dev
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>