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Re: [Question #136034]: quasi-static equilibrium

 

Question #136034 on Yade changed:
https://answers.launchpad.net/yade/+question/136034

Václav Šmilauer posted a new comment:
A few thoughts on this one, after some discussion:

1. PeriTriaxController confounds (in the mass param) static and dynamic
response of the packing, whereas they could be separated in principle.
By static, I mean stiffness, i.e. what stress delta corresponds to what
strain delta (for stress-control); to my knowledge, this is currently
computed well by Peri3dController (surrent global tangent stiffness).

2. The measure of staticity depends on the formulation used (damping,
for instance); the example Bruno gave (with free sphere rotating) is
perhaps good for cundall damping, though I would personally try to
employ another daming algorithm to get rid of the energy anyway (imagine
the sphere touches at some point another particle, and the energy is
back there -- increase in unbalanced force witout any work on the
boundary).

Intergral (over the whole system) energy measures are consistent, since
energy is what is conserved in the system. If one can formulate how much
energy can be dissipated at each simulation stage, then this can be
compared to boundary work. Currently, we compare apples and oranges
(maxStrainRate and mass for work, numerical damping for dissipation).

3. The energy "balance" between work on the boundary (increment of
meanfield kinetic energy approx, which immediately transforms in elastic
potential and fluctuation kinetic energy; real work on boundary for the
aperiodic case) and the dissipation (plasticity, damping, damage, ...)
can be written in a divergence-theorem-like form: energy flux over the
boundary (influx) = energy dissipation (efflux, or divergence) + free
energy in the system. Note that we know the influx (boundary control),
and if we can estimate the dissipation term, then the free energy
estimate is given "for free" (kinetic energy, plastic potential etc
etc).

4. If the process starts from static state (supposition), then it cannot
be static all the time (nothing would move); we need to describe the
transition static→dynamic→static, where in the first time the influx is
bigger than dissipationv in the initial "dynamization", and it inverses
for the final stabilization. The question is how much "dynamic" we want
to get in the middle phase -- it could be given by some energy measure,
such as maximum admissible energy concentration [Jm⁻³], or enegy
concentration per interaction area [Jm⁻³m⁻²].

The transition could be controlled by some smooth function f(t=0)=0,
f(t=1)=1, where t=0 is the intial static state and t=1 is the final
static state. Then f(t) would give relative predominance of dissipation
over the influx (and vice versa for 1-f(t) obviously).

Currently, only maxStrainRate controls the proportion; it is
dimensionally incorrect (wherefore the necessity for trial-and-error)
and constant (it is likely to give too low influx at the beginning, and
too high at the end -- slower-than-necessary dynamization, and slower-
than-necessary stabilization).

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