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This and the next slide are from:
K.A. Seffen and N. Borner (Dept. of Engineering, Univesity of Cambridge, UK), “The shape of helically creased cylinders”, Journal of Applied Mechanics, Vol. 80, 054501-1, September 2013,
DOI: 10.1115/1.4023624
ABSTRACT: Creasing in thin shells admits large deformation by concentrating curvatures while relieving stretching strains over the bulk of the shell: after unloading, the creases remain as narrow ridges and the rest of the shell is flat or simply curved. We present a helically creased unloaded shell that is doubly curved everywhere, which is formed by cylindrically wrapping a flat sheet with embedded fold-lines not axially aligned. The finished shell is in a state of uniform self-stress and this is responsible for maintaining the Gaussian curvature outside of the creases in a controllable and persistent manner. We describe the overall shape of the shell using the familiar geometrical concept of a Mohr’s circle applied to each of its constituent features—the creases, the regions between the creases, and the overall cylindrical form. These Mohr’s circles can be combined in view of geometrical compatibility, which enables the observed shape to be accurately and completely described in terms of the helical pitch angle alone.
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