A new triangular buckling pattern of twisted inextensible sheets

A.P. Korte & G.H.M. van der Heijden

When twisting a strip of paper or acetate under high longitudinal tension, one observes, at some critical load, a buckling of the strip into a regular triangular pattern. Very similar triangular facets have recently been observed in solutions to a new set of geometrically-exact equations describing the equilibrium shape of thin inextensible elastic strips. Here we use those solutions to construct post-buckling solutions in good agreement with the observed pattern in twisted strips. We also study the force-extension and moment-twist behaviour of these strips by varying the mode number n of triangular facets. By applying periodic boundary conditions we also compute closed strips, including knotted ones. These solutions may be relevant for graphene ribbons currently being fabricated and studied in nanotechnology.

Advances and Trends in Structural Engineering, Mechanics and Computation: Proceedings of the Fourth International Conference on Structural Engineering, Mechanics and Computation (SEMC 2010), 6-8 September 2010, Cape Town, South Africa, A. Zingoni (ed.) (CRC Press/Balkema, Leiden, The Netherlands, 2010), pp. 545-548, ISBN 978-0-415-58472-2