Guo Kexin, Suñé Marc, Kwok Ming Li, Hsia K Jimmy, Liu Mingchao, Vella Dominic
School of Mechanical and Aerospace Engineering, Nanyang Technological University, Singapore 639798, Singapore.
Mathematical Institute, University of Oxford, Oxford OX2 6GG, United Kingdom.
Proc Natl Acad Sci U S A. 2025 May 20;122(20):e2423439122. doi: 10.1073/pnas.2423439122. Epub 2025 May 12.
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 multistable morphing to kirigami grippers. Here, we demonstrate that this counterintuitive 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 tension-induced giant (TUG) folding" to reflect the importance of localized tension, and its mode of actuation and the similarity of the loading condition to 'tugging' the sheet. 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.
当沿着其最长尺寸进行压缩时，诸如扑克牌之类的薄结构会发生面外屈曲，以适应施加的压缩，而长度不会有显著变化。然而，最近的研究表明，对具有微观结构的薄片施加张力会导致从用于多稳态变形的“凹槽超薄片”到剪纸夹具等应用中的面外变形。在这里，我们证明这种违反直觉的行为——由相对较小的纵向施加张力引起的大横向折叠——也发生在各向同性材料的无结构薄片中。这种行为的关键在于局部单轴张力会引发巨大的折叠；我们将此称为“局部张力诱导巨型（TUG）折叠”，以反映局部张力的重要性、其驱动方式以及加载条件与“拉扯”薄片的相似性。我们表明，局部TUG折叠的发生是由于施加的拉伸载荷有效地转化为压缩——这是局部施加张力的几何结果。我们确定了折叠角与施加应变的比例关系，这与实验和模拟结果均相符。局部TUG折叠的普遍性质表明，它可能比以前所认识到的更广泛地应用于各种材料和结构中。
