Searching for structure Uncovering combinatorial rules to design metamaterials

Multimodal mechanical metamaterials are artificial materials that leverage geometric effects to realize multiple soft deformation pathways. Designing such materials is notoriously challenging–the space of possible geometries is vast, deformations are sensitive to small defects, and designs with the desired property are extremely rare. In this thesis, we ask how to design for multimodal metamaterials with multiple, textured shape-changes. We tackle this problem using both rational and computational methods.
First, we focus on a family of metamaterials composed of a discrete set of building blocks, and show they are capable of supporting multiple spatially extended deformations. The central challenge is to identify tilings of these building blocks that support multiple, desired deformations.
Second, we develop a method for tracking kinematic constraints in such tilings. We derive a set of necessary and sufficient conditions, or design rules, that dictate when a tiling supports a particular type of deformation.
Third, we show that convolutional neural networks (CNNs) are remarkably adapt at learning these underlying design rules from data.
Finally, we use CNNs in a data-driven design framework together with a genetic algorithm to design rare metamaterials with a high potential for spatially extended deformations. Subsequently, we refine these high potential designs to support specific deformations by strategically placing defects.
Our work enables the efficient design of multimodal metamaterials, with potential applications in soft robotics, computing in materia, and programmable materials. We also foresee applications in other fields that encounter similar combinatorial problems.