heres an interesting thought that occured to me as i was playing with this more: a zero length spring never resists compression.
so as you deform the square into a rectangle or whatever, the energy needed to stretch two side springs must be equal to the energy gained by returning the other two side springs to their natural zero length. Again, i think this is a peculiarity of zero length springs, since a normal spring would resist more as it is stretched more. But since a zip-spring has no length, there is no measure of 'how bad the spring is stretched'. the ration of natural length to stretched length is undefined. It probably works out to a constant value, which is why everything cancels out.
hope some of that was rational, Alex
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