Computationally efficient design of directionally compliant metamaterials

Designing mechanical metamaterials is overwhelming for most computational approaches because of the staggering number and complexity of flexible elements that constitute their architecture—particularly if these elements don’t repeat in periodic patterns or collectively occupy irregular bulk shapes. We introduce an approach, inspired by the freedom and constraint topologies (FACT) methodology, that leverages simplified assumptions to enable the design of such materials with ~6 orders of magnitude greater computational efficiency than other approaches (e.g., topology optimization). Metamaterials designed using this approach are called directionally compliant metamaterials (DCMs) because they manifest prescribed compliant directions while possessing high stiffness in all other directions. Since their compliant directions are governed by both macroscale shape and microscale architecture, DCMs can be engineered with the necessary design freedom to facilitate arbitrary form and unprecedented anisotropy. Thus, DCMs show promise as irregularly shaped flexure bearings, compliant prosthetics, morphing structures, and soft robots.Designing mechanical metamaterials is challenging because of the large number of non-periodic constituent elements. Here, the authors develop an approach to design arbitrarily shaped metamaterials that is more computationally efficient by six orders of magnitude compared to other approaches.