论文标题
等距，不支持的径向皱纹中的滞后波长选择
Hysteretic wavelength selection in isometric, unsupported radial wrinkling
论文作者
论文摘要
在[Pal等人，Arxiv：2206.03552]中，作者讨论了如何通过因子$δ$在其内部边界收缩的不支持的平面环，将其扣成完全等距和无张力的径向皱纹模式。在没有任何竞争性工作来源的情况下，是什么选择在这种纯弯曲配置中的波长？在本文的支持下，在数值模拟的支持下，我们认为在本地的拉伸和弯曲能量之间的竞争会导致选择波长量表$λ^* $对宽度$ w $和厚度$ t $ t $ syments commentive comments：$λ该量表$λ^*$对应于从任何波长$λ\lissimλ^*$开始的皱纹的逮捕标准，可以用大小和充满活力的障碍来解释，以进一步变高。但是，表可以支持更粗的波长：$λ\gtrsimλ^*$，因为它们的存在没有惩罚。由于这种波长选择机制取决于$λ$本身的值，因此是滞后的。
In [Pal et al., arXiv:2206.03552], the authors discuss how an unsupported flat annulus contracted at its inner boundary by a factor $Δ$, buckles into a radial wrinkling pattern that is fully isometric and tension-free. What selects the wavelength in such a pure-bending configuration, in the absence of any competing sources of work? In this paper, with the support of numerical simulations, we argue that competition between stretching and bending energies at local, mesoscopic scales leads to the selection of a wavelength scale $λ^*$ sensitive to both the width $w$ and thickness $t$ of the sheet: $λ^* \sim w^{2/3} t^{1/3} Δ^{-1/6}$. This scale $λ^*$ corresponds to an arrest criterion for wrinkle coarsening starting from any wavelength $λ\lesssim λ^*$, which can be interpreted in terms of both size and energetic barriers to further coarsening. However, the sheet can support coarser wavelengths: $λ\gtrsim λ^*$, since there is no penalty to their existence. Since this wavelength selection mechanism depends on the value of $λ$ itself, it is hysteretic.
