Programmable mechanical metasurfaces enabled by pre-compressed curved beam architectures

This work presents a comprehensive study of bistability in elastic beams, with a focus on the pre-compressed curved beam as a unique structure exhibiting both tunability and asymmetry in its potential energy landscape. Analytical modeling, supported by finite element simulations and experimental validation, reveals the conditions under which bistability emerges and defines a discriminant surface separating bistable and non-bistable regimes. Unlike conventional bistable systems that rely on lateral loading to overcome energy barriers, the pre-compressed curved beam enables an alternative stable state switching mechanism: the switching is achieved by tuning axial compression to reshape the energy landscape from bistable to non-bistable and back, enabling a controlled stable state transition. Based on this mechanism, a coupled beam design is introduced as a unit cell for constructing programmable 2D metasurfaces. The switching behavior of these units is characterized, and metasurfaces of increasing complexity are demonstrated to achieve diverse and reconfigurable patterns via boundary loading or localized expansion. These findings provide a scalable strategy for shape-programmable mechanical systems with potential applications in soft robotics, adaptive surfaces, and deployable structures.