Bistable structures, exemplified by the Venus flytrap [1] and slap bracelets (see Fig. 1), can tranform quickly from one functional shape to the other upon mechanical actuation. Potential applications can be found in mechanical/electromechanical devices from bio-inspired robots to deployable aerocraft wings. Related challenges emerged include theoretically modeling the spontaneous curving and buckling of thin objects such as leaves, flowers, nanohelices, nanoscrolls and flexible electronics [2, 3]. Despite the significant modeling efforts about such large deformation of shell structures [4, 5], the nonlinear geometric effects remain poorly understood. Here we present a continuum elasticity theory that incorporates geometric nonlinearity for large deformation of shells, and investigates, through both theoretical analysis and table-top experiments, the geometric and mechanical conditions for bistability, and the role of edge effects. Our work classifies the conditions for bistability, defines the design space for bistable morphing structures, and extends the theory of plates and shells with large deformation. A mechanical framework is provided for analyzing morphogenesis associated with growth and instability, which will also facilitate the design of multistable structures, from bio-inspired robots to deployable structures in aerospace applications.

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