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We discuss the response of thin cylindrical tubes to small indentations. Thestretching-free embedding of these surfaces is completely determined by theembedding of one edge curve, thus reducing their bending response to aneffectively one dimensional problem. We obtain that in general thin cylindricaltubes will bend non-uniformly in response to an indentation normal to theirsurface. As a consequence, their local bending stiffness, as measured byindenting at various locations along their axis, is predicted to peak at thecenter and decrease by a universal factor of 4 at either end of the tube. Thischaracteristic spatial profile of the bending stiffness variation allows adirect determination of the bending modulus of very thin tubes that are shorterthan their pinch persistence length, $l_{p}\propto R^{3/2}/t^{1/2}$, where $R$is the tube diameter and $t$ its wall thickness. We compare our results withexperiments performed on rolled-up stainless steel sheets.

Non-affine bending mode of thin cylindrical tubes