## 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