Triangular buckling patterns of twisted inextensible strips

TL;DR

This paper investigates the formation of triangular buckling patterns in twisted inextensible strips, combining experimental observations with mathematical modeling to understand the post-buckling behavior and force responses.

Contribution

It introduces a modified boundary-value problem for geometrically-exact equations and constructs solutions that match observed buckling patterns in twisted strips.

Findings

Triangular buckling patterns are confirmed in experiments.

Post-buckling solutions align with observed patterns.

Force-extension and moment-twist behaviors vary with mode number.

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 observed 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.