Combinatorial design of textured mechanical metamaterials

Lattices of cubic building blocks that deform anisotropically and that are designed to fit together like a three-dimensional jigsaw puzzle are 3D printed to create aperiodic, frustration-free, mechanical metamaterials; these metamaterials act as programmable shape-shifters and are able to perform pattern analysis. The mechanical properties of a material can be engineered by controlling its underlying architecture. This engineered architecture is typically periodic and spatially homogeneous, targeting control of the bulk properties of the material. Martin van Hecke and colleagues have developed and implemented a design principle that enables a greater degree of complexity in mechanical response: they describe a scheme for preparing mechanical 'metamaterials' possessing aperiodic architectures and for which the resulting materials are pre-programmed to give complex, spatially textured responses. When such a material is subjected to spatially patterned linear compression (using a two-dimensional array of indentations, for example), it responds by predictably shifting to a new, spatially complex shape. Such a capability could find application in, for example, soft robotics. The structural complexity of metamaterials is limitless, but, in practice, most designs comprise periodic architectures that lead to materials with spatially homogeneous features1,2,3,4,5,6,7,8,9,10,11. More advanced applications in soft robotics, prosthetics and wearable technology involve spatially textured mechanical functionality, which requires aperiodic architectures. However, a naive implementation of such structural complexity invariably leads to geometrical frustration (whereby local constraints cannot be satisfied everywhere), which prevents coherent operation and impedes functionality. Here we introduce a combinatorial strategy for the design of aperiodic, yet frustration-free, mechanical metamaterials that exhibit spatially textured functionalities. We implement this strategy using cubic building blocks—voxels—that deform anisotropically, a local stacking rule that allows cooperative shape changes by guaranteeing that deformed building blocks fit together as in a three-dimensional jigsaw puzzle, and three-dimensional printing. These aperiodic metamaterials exhibit long-range holographic order, whereby the two-dimensional pixelated surface texture dictates the three-dimensional interior voxel arrangement. They also act as programmable shape-shifters, morphing into spatially complex, but predictable and designable, shapes when uniaxially compressed. Finally, their mechanical response to compression by a textured surface reveals their ability to perform sensing and pattern analysis. Combinatorial design thus opens up a new avenue towards mechanical metamaterials with unusual order and machine-like functionalities.