Understanding a new buckling pattern of twisted inextensible strips

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.