A folded disk is bistable, as it can be popped through to an inverted state with elastic energy localized in a small, highly-deformed region on the fold. Cutting out this singularity relaxes the surrounding material and leads to a loss of bistability when the hole dimensions reach a critical size. These dimensions are strongly anisotropic and feature a surprising re-entrant behavior, such that removal of additional material can re-stabilize the inverted state. A model of the surface as a wide annular developable strip is found to capture the qualitative observations in experiments and simulations. These phenomena are consequential to the mechanics and design of crumpled elastic sheets, developable surfaces, origami and kirigami, and other deployable and compliant structures.

折叠后的圆盘是双稳态的，因为它可以弹起而变成倒置状态，其中弹性能量位于折痕上的一个很小的高度变形的区域中。当孔尺寸达到临界尺寸时，消除这种奇异性会使周围的材料松弛，并导致双稳性损失。这些尺寸具有强烈的各向异性，并具有令人惊讶的凹入行为，因此，去除其他材料可以重新稳定倒置状态。发现作为宽环形可展开带的表面模型可以捕获实验和模拟中的定性观察结果。这些现象对弄皱的弹性片，可展开的表面，折纸和折纸以及其他可展开且顺从的结构的力学和设计具有重要意义。