中心受限薄片中的起皱与可展锥
Wrinkling and developable cones in centrally confined sheets
AI总结：
本研究通过实验和分子动力学模拟探究了圆形薄片中心受限时的应力集中与图案形成过程，发现褶皱会突变为可展锥并揭示了其几何依赖性。
摘要：
薄片通过平滑起皱或将应力集中于微小尖锐区域来响应受限。从工程到生物学、地质学、纺织和艺术，薄片以多种方式被包装和受限，然而关于这些结构中应力如何集中及图案如何形成的基本问题仍然存在。利用实验和分子动力学（MD）模拟，我们探究了圆形薄片的受限响应：在其中心区域被压平并准静态地拉过一个圆环。外部自由区域先产生褶皱，随后被截顶锥取代，该锥体在向应力集中的突变转换中形成。我们探讨了与该事件相关的力及褶皱数量如何依赖于几何形状。额外的锥体依次在薄片上形成图案，直到大多数几何形状中恢复轴对称性。锥体尺寸对面内几何形状敏感。我们揭示了这种几何依赖性的粗粒化描述，它根据接近渐近 d-cone 极限（即夹具尺寸趋近于零）的程度而发散。这项工作有助于表征薄片的一般受限现象，同时拓展了对 d-cone（应力集中的基本要素）在现实环境中出现时的理解。
英文摘要：
Thin sheets respond to confinement by smoothly wrinkling, or by focusing stress into small, sharp regions. From engineering to biology, geology, textiles, and art, thin sheets are packed and confined in a wide variety of ways, and yet fundamental questions remain about how stresses focus and patterns form in these structures. Using experiments and molecular dynamics (MD) simulations, we probe the confinement response of circular sheets, flattened in their central region and quasi-statically drawn through a ring. Wrinkles develop in the outer, free region, then are replaced by a truncated cone, which forms in an abrupt transition to stress focusing. We explore how the force associated with this event, and the number of wrinkles, depend on geometry. Additional cones sequentially pattern the sheet, until axisymmetry is recovered in most geometries. The cone size is sensitive to in-plane geometry. We uncover a coarse-grained description of this geometric dependence, which diverges depending on the proximity to the asymptotic d-cone limit, where the clamp size approaches zero. This work contributes to the characterization of general confinement of thin sheets, while broadening the understanding of the d-cone, a fundamental element of stress focusing, as it appears in realistic settings.
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