Tuning stiffness of mechanical metamaterial unit cells via transitions to second-order rigid and pre-stressed states

Mechanical metamaterials have been widely studied for their broad range of exotic mechanical properties, and there is particular interest in imparting these materials with tunability to rationally alter their mechanical response on demand. Here, the concept of second-order rigidity is leveraged to design metamaterials that possess a floppy deformation mode, but that can be rigidified by altering the length of the constituent beams, such that a self-stress emerges and the floppy mode vanishes. This simple change in beam length can also give rise to controllable prestress in the material, allowing for further tuning of the elastic properties. Using a design validated with macroscopic 2D unit cells, a microfabricated 3D lattice material is demonstrated. Due to the generality of the rigidity transition, the design can be expanded to any combination of beam lengths for a given topology. Finally, a temperature-responsive hydrogel is incorporated to access the rigidity transition in situ. This design represents a simple and scalable method to assemble mechanical metamaterials with tunable rigidity.