Leembruggen Madelyn, Andrejevic Jovana, Kudrolli Arshad, Rycroft Chris H
Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.
Department of Physics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
Phys Rev E. 2023 Jul;108(1-2):015003. doi: 10.1103/PhysRevE.108.015003.
We develop an irregular lattice mass-spring model to simulate and study the deformation modes of a thin elastic ribbon as a function of applied end-to-end twist and tension. Our simulations reproduce all reported experimentally observed modes, including transitions from helicoids to longitudinal wrinkles, creased helicoids and loops with self-contact, and transverse wrinkles to accordion self-folds. Our simulations also show that the twist angles at which the primary longitudinal and transverse wrinkles appear are well described by various analyses of the Föppl-von Kármán equations, but the characteristic wavelength of the longitudinal wrinkles has a more complex relationship to applied tension than previously estimated. The clamped edges are shown to suppress longitudinal wrinkling over a distance set by the applied tension and the ribbon width, but otherwise have no apparent effect on measured wavelength. Further, by analyzing the stress profile, we find that longitudinal wrinkling does not completely alleviate compression, but caps the magnitude of the compression. Nonetheless, the width over which wrinkles form is observed to be wider than the near-threshold analysis predictions: the width is more consistent with the predictions of far-from-threshold analysis. However, the end-to-end contraction of the ribbon as a function of twist is found to more closely follow the corresponding near-threshold prediction as tension in the ribbon is increased, in contrast to the expectations of far-from-threshold analysis. These results point to the need for further theoretical analysis of this rich thin elastic system, guided by our physically robust and intuitive simulation model.
我们开发了一种不规则晶格质量弹簧模型，以模拟和研究薄弹性带的变形模式，该变形模式是施加的端到端扭转和张力的函数。我们的模拟再现了所有已报道的实验观察到的模式，包括从螺旋面到纵向皱纹、有自接触的折皱螺旋面和环的转变，以及从横向皱纹到手风琴式自折叠的转变。我们的模拟还表明，通过对Föppl-von Kármán方程的各种分析，可以很好地描述出现主要纵向和横向皱纹时的扭转角，但纵向皱纹的特征波长与施加的张力之间的关系比先前估计的更为复杂。结果表明，夹紧边缘在由施加的张力和带的宽度设定的距离上抑制纵向皱纹，但在其他方面对测量波长没有明显影响。此外通过分析应力分布，我们发现纵向皱纹并不能完全缓解压缩，而是限制了压缩的幅度。尽管如此，观察到形成皱纹的宽度比近阈值分析预测的要宽：该宽度与远阈值分析的预测更一致。然而，与远阈值分析的预期相反，随着带中张力的增加，带的端到端收缩作为扭转的函数更紧密地遵循相应的近阈值预测。这些结果表明，需要在我们物理上稳健且直观的模拟模型的指导下，对这个丰富的薄弹性系统进行进一步的理论分析。
