## Triangular buckling patterns of twisted inextensible strips

A.P. Korte, E.L. Starostin & 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
found in solutions to a new set of geometrically-exact equations
describing the equilibrium shape of thin inextensible elastic strips. Here
we formulate a modified boundary-value problem for these equations and
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
and find critical loads with jumps to higher modes.
keywords: twisted inextensible strip, triangular buckling pattern, calculus
of variations, boundary-value problem, load-displacement behaviour

*Proc. R. Soc. A.* **467**, 285-303 (2011)