A continuum description of substrate-free dissipative reconfigurable metamaterials

Reconfigurable structures have gained importance in soft robotics, for deployable and shape-morphing systems, as well as in programmable metamaterials with controllable static and dynamic properties. The fundamental building block of all such architectures is a structural unit whose tessellation results in multistability, allowing the overall system to switch between two or more equilibrium states. With increasing size and complexity, the description of those systems as discrete structures becomes cumbersome and computationally expensive (especially when considering design exploration and optimization), which is why we here introduce an effective continuum description of substrate-free (ungrounded) dissipative reconfigurable metamaterials. Passing from a discrete network to a continuum (while accounting for viscous effects in the lossy base materials) allows us to efficiently and accurately describe the time-dependent reconfiguration mechanisms. We demonstrate the performance of our approach through several examples of metamaterials and structures made of bistable unit cells in 2D and 3D, which also serve to highlight the versatility and potential of the multistable design approach towards achieving as-designed sequences of motion.