The standard methodology for this problem is to solve only for the
displacements (globally). The stresses are recomputed at the Gauss
point level. The needed history that is usually kept at the Gauss point
level is the plastic strain. Convergence is strongly tied to having a
good tangent operator; in this case you need the so-called consistent
tangent operator (see Simo and Taylor, Computer Methods in Applied
Mechanics and Engineering, 1985).
Have a look also at the comprehensive and tutorial books by Simo and
Hughes (Computational Inelasticity) and the 1st and 2nd Volumes of
Zienkeiwicz and Taylor (The Finite Element Method) now in the 7th
edition. These texts provide virtually all of the implementation
details that you need.
-sg
On 9/20/17 1:05 PM, Matthew Knepley wrote:
On Wed, Sep 20, 2017 at 12:57 PM, Maximilian Hartig
<[email protected] <mailto:[email protected]>> wrote:
On 20. Sep 2017, at 18:17, Matthew Knepley <[email protected]
<mailto:[email protected]>> wrote:
On Wed, Sep 20, 2017 at 11:46 AM, Maximilian
Hartig<[email protected]
<mailto:[email protected]>>wrote:
Hello,
I’m trying to implement plasticity using petscFE but I am
quite stuck since a while. Here’s what I’m trying to do:
I have a TS which solves the following equation:
gradient(stress) +Forces = density*acceleration
where at the moment stress is a linear function of the strain
and hence the gradient of the displacement. This works fine.
Now I want to compare the stress to a reference value and if
it lies above this yield stress, I have to reevaluate the
stress at the respective location. Then I need to update the
plastic strain / yield stress at this location.
I tried doing that first by solving three fields at the same
time: displacements, stresses and yield stress. This failed.
Then, I tried solving only for displacement increments,
storing the displacements, stresses and yield stress from the
past time step in an auxiliary field. The auxiliary fields
are updated after each time step with a second SNES, using
the displacement increments from the current, converged time
step. This also failed.
In both cases the code had problems converging and when it
did, I ended up with negative plastic strain. This is not
possible and I don’t know how it happens because I explicitly
only increment the plastic strain when the increment is positive.
I am sure there is an easy solution to how I can update the
internal variables and determine the correct stress for the
residual but I just cannot figure it out. I’d be thankful for
any hints.
It looks like there are two problems above:
1) Convergence
For any convergence question, we at minimum need to see the output of
-snes_view -snes_converged_reason -snes_monitor
-ksp_monitor_true_residual -snes_linesearch_monitor
However, this does not seem to be the main issue.
2) Negative plastic strain
This is what I’m mainly concerned with.
If the system really converged (I cannot tell without other
information), then the system formulation is wrong. Of course, its
really easy to check by just plugging your solution into the
residual function too. I do not understand your explanation above
completely however. Do you solve for the plastic strain or the
increment?
I am trying to find a formulation that works and I think there is
a core concept I am just not “getting”.
I want to solve for the displacements.
This works fine in an elastic case. When plasticity is involved, I
need to determine the actual stress for my residual evaluation and
I have not found a way to do that.
All formulations for stress I found in literature use strain
increments so I tried to just solve for increments each timestep
and then add them together in tspoststep. But I still need to
somehow evaluate the stress for my displacement increment
residuals. So currently, I have auxiliary fields with the stress
and the plastic strain.
First question: Don't you get stress by just applying a local
operator, rather than a solve?
Thanks,
Matt
I evaluate the current trial stress by adding a stress increment
assuming elastic behaviour. If the trial stress lies beyond the
yield stress I calculate the corrected stress to evaluate my
residual for the displacements. But now I somehow need to update
my plastic strain and the stress in the auxiliary fields. So in
tspoststep I created another SNES to now calculate the stress and
plastic strain while the displacement is the auxiliary field.
I’m sure there’s an elegant solution on how to update internal
variables but I have not found it.
Thanks,
Max
Thanks,
Matt
Thanks,
Max
--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to
which their experiments lead.
-- Norbert Wiener
http://www.caam.rice.edu/~mk51/ <http://www.caam.rice.edu/%7Emk51/>
--
What most experimenters take for granted before they begin their
experiments is infinitely more interesting than any results to which
their experiments lead.
-- Norbert Wiener
http://www.caam.rice.edu/~mk51/ <http://www.caam.rice.edu/%7Emk51/>
--
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Horace, Dorothy, and Katherine Johnson Professor in Engineering
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Books:
Engineering Mechanics of Deformable
Solids: A Presentation with Exercises
http://www.oup.com/us/catalog/general/subject/Physics/MaterialsScience/?view=usa&ci=9780199651641
http://ukcatalogue.oup.com/product/9780199651641.do
http://amzn.com/0199651647
Engineering Mechanics 3 (Dynamics) 2nd Edition
http://www.springer.com/978-3-642-53711-0
http://amzn.com/3642537111
Engineering Mechanics 3, Supplementary Problems: Dynamics
http://www.amzn.com/B00SOXN8JU
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