<div dir="ltr"><div dir="ltr">On Wed, Apr 23, 2025 at 2:20 PM Blaise Bourdin <<a href="mailto:bourdin@mcmaster.ca">bourdin@mcmaster.ca</a>> wrote:</div><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
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Hi,
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</div>
<div>Typically, phase-field models are formulated as rate independent unilateral minimization problems of the form</div>
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</div>
<div><span style="white-space:pre-wrap"></span>u_i,\alpha_i = \argmin_{u,\alpha \le \alpha_{i-1}} F(u,\alpha)</div>
<div><br>
</div>
<div>Where i denotes the time step. These are technically neither DAE nor ODE since there is the only time derivative in the limit model would be a constraint in the form \dot{\alpha} = 0.</div>
<div><br>
</div>
<div>The most common numerical scheme is for each time step, to alternate minimization with respect to u and \alpha. The main reason is that while F is not convex jointly in u and \alpha, it is separately convex and quadratic with respect to each variable,
and because in the simpler models.</div>
<div>Alternate minimization is technically block Gauss-Seidel, I think. It is not particularly efficient but very robust and unconditionally stable. Joint minimization in (u,\alpha) is typically fragile (most of the interesting physics in fracture mechanics
corresponds to situation where a family of critical points looses stability, i.e. the pair (u,\alpha) has to evolve through a region of non-convexity of F.</div>
<div><br>
</div>
<div>In general, is there an advantage in implementing a steady-state problem as a TS vs. Solving its optimality conditions as a SNES, or minimizing the associated energy using TAO?</div></div></blockquote><div><br></div><div>I think TAO would actually be the better route here, unless you are using time as a sort of continuation variable.</div><div><br></div><div> Thanks,</div><div><br></div><div> Matt</div><div> </div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div>
<div>Regards,</div>
<div>Blaise</div>
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<blockquote type="cite">
<div>On Apr 23, 2025, at 11:22 AM, PERRIER-MICHON Augustin <<a href="mailto:augustin.perrier-michon@ensma.fr" target="_blank">augustin.perrier-michon@ensma.fr</a>> wrote:</div>
<br>
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<br>
Dear Mr Bourdin,<br>
<br>
thank you for your answer and the remarks.<br>
<br>
I will performed time dependent multi-physics analysis including crack<br>
propagation afterward. To anticipate this time dependency, I chose to<br>
use TS solver instead of SNES or TAO. Plus, I thought that TS solver can<br>
be used for quasi-static problems as well.<br>
<br>
In my previous simulations with a monolithic TS solver, I controlled the<br>
time step during all the calculation. In my opinion I could do the same<br>
in this framework and not let TS solvers adapt the step time. A<br>
synchronization of the two solvers is necessary.<br>
<br>
With these informations, is this framework and especially TSSTEP<br>
function compatible with my problem ?<br>
<br>
Thanks a lot<br>
Augustin<br>
<br>
Le 2025-04-23 16:58, Blaise Bourdin a écrit :<br>
<blockquote type="cite">Augustin,<br>
<br>
Out of curiosity, why TS and not SNES? At the very least the damage<br>
problem should be a constrained minimization problem so that you can<br>
model criticality with respect to the phase-field variable.<br>
Secondly, I would be very wary about letting TS adapt the time step by<br>
itself. In quasi-static phase-field fracture, the time step affects<br>
the crack path, not the order of the approximation in time. I doubt<br>
that any of the mechanisms in TS are appropriate here.<br>
<br>
You are welcome to dig into my implementation for inspiration, or<br>
reuse it for your problems <a href="https://urldefense.us/v3/__https://github.com/bourdin/mef90__;!!G_uCfscf7eWS!dgihWmlH-Av_CJxXFBFTi9fkSSD7ymojR59alAozp30nnqI3OdqNX6wqPpuZ0noKSRGJ81DMvhfcxqM025KC_T1P$" target="_blank">https://github.com/bourdin/mef90</a><br>
<br>
Blaise<br>
<br>
<blockquote type="cite">On Apr 23, 2025, at 10:20 AM, PERRIER-MICHON Augustin<br>
<<a href="mailto:augustin.perrier-michon@ensma.fr" target="_blank">augustin.perrier-michon@ensma.fr</a>> wrote:<br>
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Dear Petsc users,<br>
<br>
I am currently dealing with finite element fracture analysis using<br>
phase<br>
field model. To perform such simulations, I have to develop a<br>
staggered<br>
solver : mechanical problem is solved at constant damage and damage<br>
problem is solved at constant displacement.<br>
<br>
I created 2 TS solver and 2 DMPLEX for each "physics".<br>
Each physics's system is built using TSSetIFunction and<br>
TSSetIJacobian<br>
with associated functions.<br>
<br>
The TS calls are performed with TSSTEP in order to respect staggered<br>
solver scheme in iterative loops.<br>
<br>
My question : Is the using of TSSTEP function adapted to a staggered<br>
solver ? How to use this function in my framework ? Have you got any<br>
other suggestions or advices ?<br>
<br>
Thanks a lot<br>
Best regards<br>
<br>
--<br>
Augustin PERRIER-MICHON<br>
PhD student institut PPRIME<br>
Physics and Mechanics of materials department<br>
ISAE-ENSMA<br>
Téléport 2<br>
1 Avenue Clément ADER<br>
86361 Chasseneuil du Poitou- Futuroscope<br>
Tel : +33-(0)-5-49-49-80-97<br>
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<div>— <br>
Canada Research Chair in Mathematical and Computational Aspects of Solid Mechanics (Tier 1)<br>
Professor, Department of Mathematics & Statistics<br>
Hamilton Hall room 409A, McMaster University<br>
1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada <br>
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