Understanding a new buckling pattern of twisted inextensible strips

Lead Research Organisation: University College London
Department Name: Civil Environmental and Geomatic Eng


If one twists a strip of paper under relatively high tension one observes, at acritical load, a buckling (crumpling) of the strip into a regular triangular pattern. Surprisingly, this buckling behaviour has not been reported or analysed before. The aim of the proposed work is to take advantage of recent advances in the modelling of thin inextensible sheets in order to investigate this behaviour andits implications for further structural stability and performance.The first equations for the large deformation of inextensible rectangular sheets have recently been derived by the applicant and his co-worker, supported by a running EPSRC grant. The equations have been used to solve a classicalproblem in the literature, namely that of finding the equilibrium shape of aMoebius strip. The solution shows features of bending localisation similar towhat is seen in the triangular buckling pattern of the twisted strip mentionedabove. The analogy will be used to model and analyse the new buckling pattern. The analytical results will be validated against experimental work on a purpose-built testing rig. A simplified discrete model, able to give relativelyquick approximate solutions, will also be developed and validated. The project would run in parallel with the currently-running EPSRC grant for mutual benefit.Apart from progress in our understanding of the structural stability and post-buckling behaviour of elastic sheets, the work will also give us resultswith real scope for application to modern and emerging technologies. Sheetsand strips have been observed in molecular biology and fabricated in nanotechnology. The applicant's strong links with groups in these areas willensure that potential applications will be followed up. Inextensible sheets are furthermore used widely in industry and a better understanding of their elastic behaviour will help to improve economic efficiency. The results will be particularly relevant for such modern technologies as computer-aided design and computer graphics.


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Korte A (2010) Triangular buckling patterns of twisted inextensible strips in Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

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Korte AP (2009) Curvature-induced electron localization in developable Möbius-like nanostructures. in Journal of physics. Condensed matter : an Institute of Physics journal

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Starostin EL (2011) Comment on "Statistical mechanics of developable ribbons". in Physical review letters

Description We reported and then explained a new buckling (failure) instability of thin twisted strips. The buckling pattern consists of a sequence of alternating nearly-flat triangular facets that coil around in helical fashion. The mechanical explanation is that in this way the strip can respond to a global twist by locally only bending and not stretching (the latter being energetically much more expensive than the former for a thin strip). The vertices of the triangles are found to be points of strong stress localisation.
Exploitation Route The results are relevant wherever thin sheets are subjected to twisting action; for instance in the paper and packaging industry, in sheet metal handling and in deployable structures as for instance used in space satellites.
The points of stress localisation may predict points where tearing may occur.
Sectors Aerospace, Defence and Marine,Education,Manufacturing, including Industrial Biotechology

URL http://www.homepages.ucl.ac.uk/~ucesgvd