Joining together two edges and solving for minimum energy shape 1

[apal21]

Hello,

I have a simple conceptual toy problem that I am trying to implement in Abaqus, but without success. Could someone please help me?

I have a cut sector of an annular sheet (see picture). Imagine it to be made of paper in real life. If I now bring the two edges (lying along the x-axis here) close to each other and attach them with some tape, the entire sheet will curve into a conical sector. How do I implement this problem in Abaqus? I have tried to do it with some BCs at the two edges, and with a Static, General step. But it's not working, and quits with errors.

Any ideas?

 

[FEA way]

That’s quite an interesting case. You could try wrapping it around a rigid cone in the simulation. Otherwise, you would need complex prescribed displacement BCs with proper amplitude definition (and maybe even a user subroutine).

 

[apal21]

Interesting! The rigid cone seems to be the easier solution. Could you tell me how to go about wrapping something over something else in Abaqus?

 

[FEA way]

General contact will handle all possible interactions and you just have to ensure proper movement. I think that it will be easiest to move the rigid cone towards the sheet. However, you will likely still need several BCs for the sheet so that it doesn’t just get pushed by the cone.

 

[IceBreakerSours]

Is the model supposed to replicate a manufacturing process? If yes, can you not replicate that process?

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[apal21]

No, it's just supposed to replicate my bending a sheet of paper with my hands, and then taping up two ends. Can you think of a direct equivalent to that in Abaqus?

 

[IceBreakerSours]

If I understand correctly, then that won't get done by a static analysis procedure because the physics is statically indeterminate. You definitely need inertia to stabilize the problem on top of having the right load/BCs.

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[apal21]

So you mean a dynamic, explicit analysis?

 

[FEA way]

Dynamic implicit could work too. Explicit is preferred for high-speed dynamics and highly nonlinear problems involving, for example, difficult contact conditions.

 

[IceBreakerSours]

As FEA way pointed out, either explicit or implicit time integrator will work.

Although I agree with FEA way about explicit, the conversation is richer: Explicit might offer a more "predictable" route over the course of a project; implicit needs a fair degree of patience, baby-sitting, and re-work if changes are made to the original model set-up. However, if you have not used explicit before, then you are in for a ride and you have to pay close attention to the results because explicit does NOT enforce equilibrium. It sounds scary but, with experience, explicit is a valuable tool - just like implicit statics or implicit dynamics. [Note: Static procedure is an implicit scheme; time is not physical but a load/BC scaling factor.]

Opinion: I know I am in a minority but I don't care a lot for static procedures - Inertia stabilizes the model without having to resort to numerical magic tricks like contact stabilization.

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[apal21]

@IceBreakerSour, what exactly do you mean when you say Explicit does not enforce equilibrium? It time-integrates Newton's second law, so that is enforcing force balance, and hence equilibrium, at every step right. Right?

Also, what does stabilisation through inertia mean? Shouldn't greater inertia (aka mass) lead to waves and instabilities ?

 

[FEA way]

Abaqus/Explicit solves for true dynamic equilibrium. Quasi-static analyses can be performed using this solver (and it's very often done) but you have to make sure that the inertia doesn't become too significant. For this purpose, a careful examination of whole model energies is necessary.

Inertia stabilizes the model in terms of its rigid body motions that often occur before the contact is established. There are some special features to handle that (automatic stabilization in step settings or contact stabilization) but it's often better to just switch to quasi-static analysis using a dynamic solver.