In this article, we unravel an intimate relationship between two seemingly unrelated concepts: elasticity, that defines the local relations between stress and strain of deformable bodies, and topology, that classifies their global shape. Focusing on Möbius strips, we establish that the elastic response of surfaces with nonorientable topology is nonadditive, nonreciprocal, and contingent on stress history. Investigating the elastic instabilities of nonorientable ribbons, we then challenge the very concept of bulk-boundary correspondence of topological phases. We establish a quantitative connection between the modes found at the interface between inequivalent topological insulators and solitonic bending excitations that freely propagate through the bulk nonorientable ribbons. Beyond the specifics of mechanics, we argue that non-orientability offers a versatile platform to tailor the response of systems as diverse as liquid crystals and photonic and electronic matter.

中文翻译：

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不可定向带的拓扑弹性

在本文中，我们揭示了两个看似无关的概念之间的密切关系：弹性（定义可变形体的应力和应变之间的局部关系）和拓扑结构（对它们的整体形状进行分类）。着眼于莫比乌斯带，我们建立了具有不可定向拓扑结构的表面的弹性响应是非加性的，不可逆的并且取决于应力历史。调查不可取向的带的弹性不稳定性，然后我们挑战拓扑相的体边界对应的概念。我们在不等价的拓扑绝缘子与孤子弯曲激发之间的界面处发现的模式之间建立了定量的联系，孤子弯曲激发自由地散布于整个不可定向的带中。除了力学的细节之外，