We establish a theoretical framework for large deformation of plates and shells that incorporates geometric nonlinearity, which is applied to study bistable structures. Our work classifies both geometric and mechanical conditions for bistability, and defines the design space for bistable morphing structures. Theoretical predictions are validated through tabletop experiments. This work also advances the understanding of plates and shells with large deformation, as well as the mathematical concept of developable and non-developable surfaces in the physical world. The results of our work will also promote understanding of morphogenesis in a variety of natural and engineered systems and facilitate the development of smart bio-mimetic devices as sensors, actuators, energy harvesting devices, artificial muscles, and bio-inspired robots.
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