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)