Andrejevic Jovana, Lee Lisa M, Rubinstein Shmuel M, Rycroft Chris H
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA, USA.
The Racah Institute of Physics, The Hebrew University of Jerusalem, Jerusalem, 91904, Israel.
Nat Commun. 2021 Mar 5;12(1):1470. doi: 10.1038/s41467-021-21625-2.
As a confined thin sheet crumples, it spontaneously segments into flat facets delimited by a network of ridges. Despite the apparent disorder of this process, statistical properties of crumpled sheets exhibit striking reproducibility. Experiments have shown that the total crease length accrues logarithmically when repeatedly compacting and unfolding a sheet of paper. Here, we offer insight to this unexpected result by exploring the correspondence between crumpling and fragmentation processes. We identify a physical model for the evolution of facet area and ridge length distributions of crumpled sheets, and propose a mechanism for re-fragmentation driven by geometric frustration. This mechanism establishes a feedback loop in which the facet size distribution informs the subsequent rate of fragmentation under repeated confinement, thereby producing a new size distribution. We then demonstrate the capacity of this model to reproduce the characteristic logarithmic scaling of total crease length, thereby supplying a missing physical basis for the observed phenomenon.
当一个受限的薄片起皱时，它会自发地分割成由脊网络界定的平面小面。尽管这个过程看似无序，但起皱薄片的统计特性却表现出惊人的可重复性。实验表明，当反复压实和展开一张纸时，总折痕长度呈对数增长。在这里，我们通过探索起皱和破碎过程之间的对应关系，来深入了解这一意外结果。我们确定了一个用于描述起皱薄片小面面积和脊长度分布演化的物理模型，并提出了一种由几何挫折驱动的重新破碎机制。这种机制建立了一个反馈回路，其中小面尺寸分布决定了在反复受限下后续的破碎速率，从而产生新的尺寸分布。然后，我们证明了这个模型能够重现总折痕长度的特征对数缩放，从而为观察到的现象提供了缺失的物理基础。
