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In summary, when I squeeze the balloon, it changes its shape from a sphere to a pancake. The stored elastic energy is a function of the surface area of the balloon.f

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I do not think it will be the same, as I'm stretching the material. I'm assuming a rubber balloon material.

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So a complete solution will require either simplifying assumptions or a careful description of the deflection.

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And do you think all rubber has the same elasticity/strength?I do not think it will be the same, as I'm stretching the material. I'm assuming a rubber balloon material.

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YesAnd do you think all rubber has the same elasticity/strength?

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Then you would do well to do a bit more research.Yes

Look, I'm asking you these leading question trying to get you to arrive at the obvious conclusion that your "problem statement" is so ill defined that it's approximately like asking "how high is up?" and expecting a meaningful answer.

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So a complete solution will require either simplifying assumptions or a careful description of the deflection.

This kind of assumptions are correct?:

I should say It worth, it's part of a research I'm starting and I want to be sure that I'm handling this problem in a proper way.

Could you help me, how can I start?

Thanks

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I would start by developing the strain energy equation for the rubber as a function of the three principal stretches. The rubber deformations in your application may be large, so you can't use the small strain approximations to describe the rubber elasticity behavior, and you can't use a one dimensional version because the local deformations are going to be 3D.

The behavior the the glass bead gravel inside the ball is going to be complicated, so you can start out by researching the rheological behavior of non-consolidated granular solids.

Temporarily, before including the glass bead behavior in the model, you should consider assuming there is air inside. At least then the behavior of the material inside the ball would be simple to include. You can switch to granular beads later.

You also need to start formulating the stress equilibrium equations for the rubber cover, treating either as a membrane or a shell. A membrane is, of course easier to solve.

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I would start by developing the strain energy equation for the rubber as a function of the three principal stretches. The rubber deformations in your application may be large, so you can't use the small strain approximations to describe the rubber elasticity behavior, and you can't use a one dimensional version because the local deformations are going to be 3D.

The behavior the the glass bead gravel inside the ball is going to be complicated, so you can start out by researching the rheological behavior of non-consolidated granular solids.

Temporarily, before including the glass bead behavior in the model, you should consider assuming there is air inside. At least then the behavior of the material inside the ball would be simple to include. You can switch to granular beads later.

You also need to start formulating the stress equilibrium equations for the rubber cover, treating either as a membrane or a shell. A membrane is, of course easier to solve.

Thank you very much for your help, this information is helpful to me.

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