Corrugated Sheets with Loading-Position-Dependent Bistability

Structures capable of multiple stable configurations are increasingly attractive for applications in shape-morphing and adaptive systems. Among these, corrugated sheets are promising due to their ability to achieve different loading-position-dependent stable morphologies. In this work, the bistability of corrugated sheets is systematically investigated, where point loads at different positions can lead to distinct stability responses. To quantify the mechanical behavior, a theoretical model of the sheet is developed, combined with finite element analysis (FEA) and experimental validation. The analysis begins with a single-cell model, from which a phase diagram is derived for the transition between monostable and bistable regimes as a function of nondimensional geometric parameters. The model is then extended to multi-cell corrugated sheets to reveal the effects of intercellular interactions on the overall stability landscape of the structure. Finally, the theoretical model enables customization of bistable regions in the corrugated sheets—such as butterfly-like and diamond-like bistability regions—achieving programmable bistability through the geometric design of unit cells and their spatial arrangement. This work provides insights into how loading position influences the mechanical stability of corrugated sheets, presenting significant potential for advanced applications in shape-morphing structures, soft robotics, and sensor technologies, where tailored mechanical responses are crucial.