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Arc Length Continuation method fails at low arc length values.

maharshi.kintada's picture

I have implemented a Arc length continuation method for material non-linearity. The program quits with low arc length values while it progresses well for high arc length values. I am attaching a png image for your understating  about the nature of the force deformation curve. Can you please clarify me about the problem and provide me any suggestions on it.

Thanks in advance.

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Arc_length_comparsion28.14 KB

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maharshi.kintada's picture

Your suggestions are valuable.

From your first curve with larger arc length it seems that there is a snap-back. Traditional

arc-length method would also fail in case of a snap-back. Try first very very small arc-length beyond the softening regime and see?

Also did you try the modified arc-length methods. I suspect that due to strain softening in your problem, the snap-back response may be difficult to track. You may want to also play around with the arc-length to get more insight.I think the convergence is not occurring because the next equilibrium point is too far away.

Also did you try the modified arc-length methods. I suspect that due to strain softening in your problem, the snap-back response may be difficult to track. You may want to also play around with the arc-length to get more insight.I think the convergence is not occurring because the next equilibrium point is too far away.

maharshi.kintada's picture

Thanks for quick response. You are right, the next equilibbrium point is far from the converged last one. If you think modified arc lengths solve this issue. can you please refer one such technique please.

I think there are many arc length methods. Ramms arc-length method or modified riks method. Crisfields arc-length method might also be checked. But i think for problems with strain-softening, as it appears to be your case, it might be that even the arc-length method fails. But you really need to try it out as they have different type of constraint controls. 

maharshi.kintada's picture

Very very small arc length too fails. I tried 0.0001 too. I got the same peak to be last converged point.

This is then definitely a case of so-called snap-back. Here both the force and displacement decrease simultaneously. This may be due to a material non-linearity like crack-propagation and subsequent relaxation of the material.

As I mentioned in my previous post, there are certain methods for the material non-linearities.
Crisfields arc-length method may be handle it. Also there are a few more dedicated for material nonlinearities

and may not be implemented in the commercial solvers.

 

maharshi.kintada's picture

Thanks for your response.

As per your suggestion I implemented the modified arc length by,

A new arc-length method for handling sharp snap-backs by H.-B. Hellwega,M.A. Crisfieldb

The above method also showing a disadvantage i.e.,

In the initial linear elastic region, the both roots are almost equal and this method back marches the solution.

After any equlibrium point in the path, It may take roots which follows back the same travelled path.

Can you please comment on this, your suggestions are so valuable.

Hi, It would be difficult to comment anymore without looking at the problem. I will try to make an educated guess.

It is possible that your problem also involves buckling so that there are alternative solutions. With the crisfield method you may have a problem with an incorrect predictor which is taking you back on its path.  

What kind of material do you have? If you want you can mail me some details on loginforlammps at gmail dot com.

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