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Does numerical dissipation in FE simulations affect system's elastic energy? Does it depend on thick

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Did you verify other results of this analysis ? Especially energies as those are available in various forms in Abaqus. For example you can plot energies dissipated by each phenomenon. I would also try running this simulation with different solver settings.
 
On that other forum you’ve mentioned that you already tried the explicit solver. But there are also other possibilities like general static analysis, with or without stabilization. There are several ways to handle highly nonlinear problems and instabilities like that in Abaqus.
 
The static solver didn't work. The job ended with an error before even finding any wrinkling. Can you suggest any other solvers?
 
Static solver will most likely need some aid to handle instability. If automatic stabilization that can be defined in step settings doesn’t help, you can try the Riks (arc-length) solver. It’s a separate type of step.
 
I am not sure I understand why the explicit scheme did not work. As was suggested, did you try plotting out various energies that /Explicit makes available to you?

That said, yes, dissipation does have an impact on physical energies but the degree to which has an impact is the key thing to focus on. And that only you can be the true judge of but the thumb rule is that if numerical juices are below 5% of the physical energies, then you are fine. I think that is a safe bet given that, for instance, multiple inputs to the model are likely to have variabilities associated with them.

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I have plotted out various energies in both Implicit and Explicit, but none of them seem to tell me anything about numerical dissipation. Among all the energies here ( the only ones of any importance to my case seem to be ALLIE, ALLKE, ALLWK and ETOTAL. ALLKE I keep very small. Thus, if there is any difference between ALLIE and ALLWK, it seems to show up in a non-zero ETOTAL. There are no contact penalties or anything like that.

Is there some particular variable that tracks numerical dissipation due to the solver itself?
 
Try modeling a swinging pendulum and see how long the swinging goes. As you must know, without any physically dissipative effects, the swinging should go on forever.

While you are doing that, look for half-step residual in the theory manual for Abaqus and read up on it.

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