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Here are two examples:

https://www.comsol.com/model/spherical-cap-with-central-point-load-67161

https://www.comsol.com/model/postbuckling-analysis-of-a-hinged-cylindrical-shell-10257

Thank you sir! I have reviewed these 2 models and I found the second one similar with my problem. However, the second model is time-independent. Do we have arc length method implemented for time-dependent problems? Thanks.

In a time dependent analysis, the inertia will stabilize the structure. You can just use a load that increases with time.

That is what happens during a snap-through event in real life: When the limit point is reached, the applied load is balanced by inertial forces. See the attached plot. The vibrations is what causes the characteristic sound emission.

In a time dependent analysis, the inertia will stabilize the structure. You can just use a load that increases with time.

That is what happens during a snap-through event in real life: When the limit point is reached, the applied load is balanced by inertial forces. See the attached plot. The vibrations is what causes the characteristic sound emission.

Thank you very much!

Hi! I have tried this method and also the parametric sweep and they work under the assumption that the loading type is force. However, I still have one question, what if the loading type is prescribed displacement? For example, in the first pitcure is an single edge notched specimen under tension and the loading condition is a prescribed displacement on the upper bound. In my time-dependent simulation, I used displacement control and the computation diverges as the second pitcure indicates and I think it is because equilibrium path has a snap-back behaviour. So how can I use arc length method in this example when the loading condition requires that the upper bound of the specimen moves identically in the y direction? Thank you again for your patience.

I guess that you are working with a deteriorating material model, like a cohesive zone model. That is a much nastier type of 'negative stiffness' than the ordinary snap-through problem. The negative stiffness will occur locally in several elements, and it can be extremely difficult to find a solution.

If you do it in time domain, stress waves will start traveling from the crack tip, out to the boundaries, and then be reflected back.

In this case, you may need some regularization method, like the ones available in the Damage material model, or in Decohesion under Contact.

I guess that you are working with a deteriorating material model, like a cohesive zone model. That is a much nastier type of 'negative stiffness' than the ordinary snap-through problem. The negative stiffness will occur locally in several elements, and it can be extremely difficult to find a solution.

If you do it in time domain, stress waves will start traveling from the crack tip, out to the boundaries, and then be reflected back.

In this case, you may need some regularization method, like the ones available in the Damage material model, or in Decohesion under Contact.

Thanks for your reply. I am doing quasi-static analysis of a cohesive zone model implemented with phase field method. The post-peak behaviour is very unstable and the author of the paper mentioned that CMOD control should be used to track the post-peak behaviour. I tried parametric sweep with force type loading condition and it works well but I don't know how to use this method with displacement type loading condition.

I have never seen an example where a prescribed displacement is controlled in this way. It is possible that there can be some subtle reason for why it would be problematic. If so, you can try replacing the prescribed displacement with a rigid connector, and control the force on the rigid connector from the CMOD. But that is just a guess from my side.

I have never seen an example where a prescribed displacement is controlled in this way. It is possible that there can be some subtle reason for why it would be problematic. If so, you can try replacing the prescribed displacement with a rigid connector, and control the force on the rigid connector from the CMOD. But that is just a guess from my side.

Got it. Thank you very much!