Mechanical metamaterial systems as transformation mechanisms

Research in mechanical metamaterials has achieved extreme, unprecedented properties by exploiting inhomogeneity in the form of periodic structures, enabled by advances in digital computation and manufacturing. The result has been a proliferation of metamaterials and relatively recently, the emergence of non-periodic heterogeneous metamaterial systems, which we term metastructures. This represents the beginnings of the evolution of metamaterials from just materials with unique properties towards systems capable of more complex, machine-like functions. To better understand the essential features and relationships among this wide and growing variety of species within the classes of mechanical metamaterials and metastructures, a classification scheme that focuses on functionality is needed. Both periodic and non-periodic metamaterials systems can be abstracted as mechanisms that produce desired outputs by performing specified transformations on given mechanical inputs. Here we propose an approach to functional classification and comparison based on the deformation and force transformations that these metamaterials and metastructures can provide. Transformation- based approaches are prevalent in geometry processing, computer graphics and soft robotics. This review examines existing periodic and non-periodic metamaterials from this perspective, classifying them according to the quasi-static deformation output they can achieve, and identifying gaps, challenges and promising future directions. Two classes of transformations are defined, i.e., uniformly distributed (homogeneous) or spatially dependent (non-homogeneous), and their building blocks and mechanisms are discussed. This stance empowers a more efficient approach to inverse design of metamaterial systems, in which desired operations are realized through transformations produced by the combination of diverse building-block architectures.