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I have a 20x20cm piece of foil with a circular hole of diameter 1cm in the centre.

If I slowly stretch the foil both horizontally and vertically, what happens to the size of the hole?

Does the size of the hole change? If the foil doubles in size to 40x40cm, will the hole be of diameter 2cm? Do any factors affect the size of the hole? The temperature of the room, the speed at which I stretch the foil?

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dplanet: There are far too many unspecified properties in play in the version of the question you are asking, e.g. metal foil will rip, very soft materials will stretch at the edges only, anisotropic materials will behave differently along different axes, and a rather select group of "latex like but less prone to tearing" materials will approximate your proposed outcome. –  Terry Bollinger Apr 12 '12 at 0:23
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If it's a uniform metal, the hole will stretch just like the rest of the sheet. If you "filled in the hole" with a piece of foil, such that the sheet was now complete, the sheet would stretch uniformly. Now imagine changing the size of the hole, and/or "filling it in" again, only this time not connecting the filled in piece to the rest of the sheet. If you heat it, all the metal expands, even the metal in the hole. The only way of thinking about it that leads to the sheet not overlapping itself is to admit that the hole grows as well.

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That's true for heating, but stretching is different, because stress can't flow through the hole easily. The stress profile is a little annoying to solve, but in general it should still qualitatively stretch. –  Ron Maimon Apr 12 '12 at 2:02
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