Geometrically Frustrated Mechanical Metamaterials

Mechanical metamaterials are built of repeating macroscopic unit cells, and are designed so that their cooperative local deformations will lead to unusual mechanical behavior at the system level. We focus on two- and three-dimensional structures with anisotropic unit cells. When the orientation of each one is set at random they typically form an aperiodic structure, in which adjacent unit cells may not all deform self-consistently, thus constituting a mechanical spin glass. By mapping to discrete spin models, we present a combinatorial strategy for the design of a multitude of aperiodic, yet frustration-free metamaterials that exhibit spatially textured functionalities. We demonstrate these by designing three-dimensional metacubes, which when compressed can deform to give any pre-defined texture on their faces. Moreover, we quantitatively explain how pressing on a metacube with the wrong texture increases its overall rigidity. Finally, in two-dimensions we construct topological defects which give rise to multistability reminiscent of multiple metastable states in glasses.