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I am interested in the following problem: starting from a flat sheet, once can bend it into a (sector) of a cylinder isometrically. If further (orthogonal to the first plane) curvature is induced, the sheet will necessarily be stretched. The question is, how much stretch is locally caused by the increase in curvature? I could attempt to answer the point by classical continuum mechanics tecniques, but I am told differential geometry allows an answer to be given immediately. Could somebody please point me towards the answer, or suitable material to study? Many thanks

Smerdjakov
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    I am not sure, but maybe this question is more suited for http://math.stackexchange.com/ ? – Hunter Jan 27 '14 at 15:09
  • What is the actual question here? Material behavior varies greatly and differs from topological behavior in mathematics. – Carl Witthoft Jan 27 '14 at 15:34
  • I apologise for the confusion, I am not interested in material behaviours in an engineering sense. The question could be rephrased as follows: given a flat sheet, this is locally deformed such that the two principal curvatures are known. Such deformation is not isometric: How to relate the stretch induced by it to the curvatures values? – user37155 Jan 27 '14 at 19:43

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