Triangular buckling patterns of twisted inextensible strips

A. P. Korte, E. L. Starostin, G. H. M. van der Heijden

Abstract

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.

  • Received April 13, 2010.
  • Accepted May 26, 2010.
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