Memory in non-orientable mechanics

Non-orientability is a topological property, which presents it is unable to make a consistent choice of surface normal vector at every point. Because of this non-trivial topological property, non-orientability can create novel and unusual mechanical behaviour. However, the complex geometry of non-orientable structures limits their applications in the real world. Here we show that it is possible to achieve non-orientable mechanics in an orientable metamaterial, rotating-square mechanism. This is achieved by a geometrical frustration, which generates a single movable domain wall in periodic structures during loading. The moving path of the domain wall can be controlled by the loading sequence, which leads to different mechanical responses. In other words, our metamaterial can break abelian rules and has a mechanical memory. Based on it, we build a mechanical sequential logic gate, which can achieve the same value table as with a Set-Reset latch, one of the most basic sequential logic gates in electronic fields. The geometrical frustration design opens up a new avenue for new design of topological metamaterials, non-orientable metamaterials, non-abelian metamaterials and sequential logic gates.