Tunable Mechanical Metamaterials from Second Order Rigid Unit Cells

Mechanical metamaterials derive their unusual mechanical properties from their deliberate structuring as opposed to the bulk properties of their constituent materials. Their design can enable unique behaviors such as negative effective moduli and auxeticity, however, these behaviors are often static and cannot be tuned once the material is assembled. Thus, there is considerable interest in enhancing the functionality of mechanical metamaterials by incorporation of tunable or shape changing elements to adjust their mechanical response on demand. Here, we demonstrate a mechanical metamaterial that can be switched from floppy to rigid by leveraging second order rigidity. We design square unit cells containing a system of 3D printed beams and joints that are predicted to be floppy by simple constraint counting. However, by altering the lengths of the beams, the structure will pass through a critical point where it will suddenly rigidify. We exhibit that this behavior is general for any combination of beams lengths, and finally, we show that the beams can be made from a temperature-sensitive hydrogel, whereby heating of the unit cell will result in shrinking of the beams and subsequent rigidification of the structure.