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Re: dissipating all energy in a packing
This is a very interesting problem, but honestly I thought to this hard
(and I tried many different dampings on 1D oscillators) and couldn't
find any good idea. I always end with the basic Cundall's damping being
the most efficient and versatile damping.
2. I could try to make cundall's damping to always diminish the force
iff the coefficient is <0 (.e.g damping==-.3 would mean to always reduce
the force to ×.7), what do you think?
I'm still open to suggestions though.
Note that these 2-steps oscillations are sensitive to the time
increment, so it is just one more aspect of numerical instability with
inapropriate timesteps (and in fact, I think Cundall's damping is so
that if the undamped scheme is stable, the damped scheme will be stable
too, I have no instant-proof of that though). The only question is : can
damping revert the velocity to a greater opposite value in one (or even
two) step? In principle it can not.
If I understand the idea above correctly, you would multiply all forces
by 0.7 whatever the direction relative to velocity?
Well, in one sense, it would just mean a change in timescale (slowing
down all motions by a factor of 0.7...).
The problem is it would damp no energy at all.
In terms of stability, it would have exactly the same effect as
decreasing the time increment.
What value are you using for damping?
In order to decrease kinetic energy even more (you need to normalise
kinetic energy with elastic energy btw, or you can't tell if the value
is "high" or "small", why do you say it's not small enough?), I would
set it to something around 0.1, and I would try reducing the timestep by
a factor of ~0.8.
It is useless to increase the damping to higher values in most cases.
The PFC default : 0.7, is some of the worst idea they had if you ask me.
Higher (than the optimal value) damping means slower convergence to
equilibrium when "convergence" implies some rearangements in the packing
(instead of just damped oscillations in a completely elastic problem).
When you are close to equilibrium, you always have this last grain that
will move a little, then trigger a local instability that will spread to
all the sample, which leads to small changes in each particle's
equilibrium state. This is the sort of events that can be a lot slower
with a large damping.
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