This is a reference request for a theory of bursting balloons:

Let's say I have a balloon and this balloon has an impurity along a small strip. Let's assume for example the balloon had a hole there at some point and I tried to fix it with some tape. So the structural properties of the balloon are very different in that particular area. So now I start blowing up my balloon until it explodes.

My question is: Does there exist a theory that based on some assumptions on the overall material properties of the balloon will allow me to model

  • a) where it will burst and

  • b) how, i.e. how will the hole extend?

Ab initio answers on some of your own ideas how to model this are of course also welcome!

I understand that the question is not a well-defined homework problem and there may not be an optimal answer, but I would be grateful to some pointers to equations and theoretical methods to study the bursting mechanism.

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    $\begingroup$ There is a reasonable amount of work around rips, tears, cracks, etc. The basic idea is that when one of these cracks is in progress, the forces become concentrated towards the vertex of the crack. Therefore, once the crack is started, it continues. Does this give you enough to look up what you need, or are you looking for something else? $\endgroup$ – tom10 Apr 3 at 21:27
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    $\begingroup$ @tom10 Thank you for looking at my question: I think I would like to know a) how to model where the rip forms and then b) how it will continue. Are there any good theoretical models for that? $\endgroup$ – Martinique Apr 3 at 21:28
  • $\begingroup$ Generally, reference requests are off topic. For questions like this, it makes sense to me. In what way would someone doing a search for "physics of cracks", "fracture mechanics", etc, be better for you than you doing the same search? If I understood that, I might be able to help. $\endgroup$ – tom10 Apr 3 at 22:32
  • $\begingroup$ @tom10 well, if I look at most references, then I see two problems: a) They do not seem to treat the question where does the crack form, at least on the wikipedia article to fracture mechanics I could not find this and b). most of it seems to be developed more for solid materials like metals. Can you comment on that?- I for example also found this and do not know if it is maybe more useful for my purposes: en.wikipedia.org/wiki/Peridynamics $\endgroup$ – Martinique Apr 3 at 22:37
  • $\begingroup$ "physics tear elastic sheet" gives this pdf as the first hit and fig 2f even shows an expired balloon. Anyway, I don't think I can do this better than you. You just have to try. $\endgroup$ – tom10 Apr 3 at 23:48

a) where will it burst?

The 'burst' would start at the weakest part of the balloon, for example where there is a small defect or perhaps where it was mended as you described.

b) how will the hole extend?

If you look at burst balloons, you'll see a rip, approximately in a straight line. To imagine why this happens, imagine pulling both ways on a strip of paper, it could be quite strong and hard to rip. If there is a small cut on one edge, a tear would start there and move along - the paper tears into two pieces, approximately in a straight line.

Which line a 'tear' in the balloon starts to move would depend on the strength of the material around the initial starting point. Once it starts tearing in a direction, it's more likely to continue in a similar direction, as a tear in a piece of paper does.


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