I'm not a materials scientist, so I probably don't really know the right answers to these questions or what the correct terms are. All I can do is try give you an idea of what happens in practice from my limited experience, and my working understanding of it.

> I think a more refined version of your parent poster's question might be, why doesn't the gasket continue to extrude itself out of the gap, even though its ultimate strength has been exceeded by possibly several orders of magnitude?

It does continue to extrude itself out of the gap. The more you increase the pressure, the more gasket material comes out. And this isn't an elastic, reversible process - it's plastic deformation which leaves the gasket permanently thinner after you unload the cell. So the gasket material has failed, in terms of what we'd usually use "failure" to mean in an everyday mechanical structure.

But your expectation seems to be that beyond the point of failure, the gasket material should basically just flow freely, like a liquid. That's not what happens. Failure is just the point at which permanent damage starts to occur. There's a whole separate region of behaviour beyond that point, which depends on the material and the conditions.

I mentioned that in this work, they go beyond the yield strength of diamond. If you look at Fig 6 in the actual paper [0], they have an electron microsope image of the diamond tip after unloading the cell. It's permanently and severely damaged, with concentric ring cracks around the tip. So the diamond did "fail", in the formal sense of that word. But that doesn't mean it didn't do the job they needed it to do anyway.

> You could say the small center area of pressure is acting on a very thick cross-section of gasket (like a big pipe with a tiny inside diameter), but isn't there a limit to this where the pressure doesn't care how much extra material you pile on?

There probably is! But that's not what failure means, and so it's not what numbers like yield strength refer to. Failure for your big pipe is the point at which the internal pressure starts to permanently bulge the pipe. It's not necessarily the point at which it ruptures. That can happen at any point beyond failure, depending on the material and the conditions.

> Or for a more layman example, Jello has some amount of tensile strength, but you can't exactly build a cannon out of it regardless of how thick the barrel is. Metal at these pressures probably behaves more like jello than metal, so what's keeping it together in this case?

Let's take a layman's example that better fits the question at hand, and requires a bit less hypothesising about jello.

Rubber has some amount of tensile strength, but you can't build a car's engine block out of it.

It works just fine for the head gasket, though, where it has to successfully contain the extreme pressures that occur in the cylinders during the combustion cycle. It works in practice in the conditions where it's compressed between the head and the block.

And that's exactly the role that the rhenium gasket plays in a DAC.

In both cases, there is some pressure beyond which it will no longer do the job. But there probably isn't a simple number you can look up which will tell you when that will happen, based only on the material.

[0] https://sci-hub.se/https://doi.org/10.1038/s41586-019-1927-3