Localized tension-induced giant folding in unstructured elastic sheets

Abstract

Buckling in compression is the archetype of elastic instability: when compressed along its longest dimension, a thin structure such as a playing card will buckle out-of-plane accommodating the imposed compression without a significant change of length. However, recent studies have demonstrated that tension applied to sheets with microscopic structure leads to out-of-plane deformation in applications from `groovy metasheets' for multi-stable morphing to kirigami grippers. Here, we demonstrate that this counter-intuitive behavior -- a large transverse folding induced by a relatively small imposed longitudinal tension -- occurs also in unstructured sheets of isotropic material. The key to this behavior is that a localized uniaxial tension induces giant folding; we refer to this as `localized TUG folding' to reflect the importance of localized tension and its mode of actuation. We show that localized TUG folding occurs because of an efficient transfer of applied tensile load into compression -- a geometric consequence of a localized applied tension. We determine scaling results for the folding angle as a function of applied strain in agreement with both experiments and simulations. The generic nature of localized TUG folding suggests that it might be utilized in a broader range of materials and structures than previously realized.