Suppose I have a uniform, well annealed metal cylinder with a scratch on its surface. Can I predict geometry of how it will buckle under compression if I know the exact geometry of the scratch and there are no other scratches? Cc:
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Not really. A collapse like that is a chaotic process, so details matter and models tend to ignore them. I.e. Earth is a spherical planet in a vacuum. You can precisely calculate how lobbing an asteroid at it would change its orbit. But try it and your rock gets nuked. Same here.
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But clearly the chaotic process will go from being sensitive to initial conditions to insensitive as scratch size goes. A deep enough scratch should nearly deterministically buckle on that side. Like in picture.
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I only have one semester of metallurgy in my past, and this is one of those spherical cow physics-perfect things, but I would say generally yes.
in real life you'll never have perfect anneals or perfect alloys or grain structures etc. so there's some statistical accuracy there
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I would guess so. In general a cylinder should have a (probably continuous) set of preferred buckling modes. A defect will make one of these modes preferred energetically over the others in a way that's probably not hard to figure out.
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Sounds like a problem where this might lead to a good enough approximation: en.m.wikipedia.org/wiki/Finite_el
I can recommend z88.de
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Newton says yes, quantum theory says no, Schrödinger suggests there is no way to know for sure.
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