By inward inflation, I mean vacuum inside the membrane (such as a cylinder with closed ends) leading to its crushing by atmospheric pressure.
Dear Mr Reddy,
It depends on how vacuum is created.
Consider a plastic can with liquid subjected to lowered temperature.
Is that a case, within your study?
Dear MS. Stromberg,
Let's say the air inside the membrane is pumped out to create a vacuum or equivalently, higher pressure is created around the membrane to crush it in. No liquids involved.
I want to know whether we can find minimizers of total potential energy (elastic strain energy + pressure work) in this case. I programmed the mathematics for outward inflation. When the inflating pressure is negative, no equilibrium is found.
Thanks very much for your time.
A membrane theory is not suitable in this case since a membrane cannot support compression. Therefore, what you want is an elastic shell or a cylindrical shell. The case of a cylindrical shell under pressure is known and leads to build-up of compressive stresses. Crushing will depend on inhomogeneities and is much harder to predict. Similarly the crushing of an elastic shell is a difficult problem. Recent work by Thompson and Hutchinson on nonlinear shells under pressure is relevant for you.
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